Deck 24: Trigonometric Functions The Unit Circle

Question 1

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = \frac { 25 \pi } { 3 }$ ​

A) $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\\tan \left( \frac { 25 \pi } { 3 } \right) = - \sqrt { 3 }\end{array}$
B) $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \\\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }\end{array}$
C) $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\\\\cos \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 } \\\\\tan \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 3 }\end{array}$
D) $t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 25 \pi } { 3 } \right) = - \frac { 1 } { 2 } \\\\\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\\\\tan \left( \frac { 25 \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 3 }\end{array}$
E)Not possible

Answer 1

$t = \frac { 25 \pi } { 3 }$ corresponds to the point $( x , y ) = \left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 25 \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 } \\\cos \left( \frac { 25 \pi } { 3 } \right) = \frac { 1 } { 2 } \\\tan \left( \frac { 25 \pi } { 3 } \right) = \sqrt { 3 }\end{array}$

Question 2

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 10 \pi } { 3 }$ ​

A) $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ .
B) $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ .
C) $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .
D) $t = \frac { 10 \pi } { 3 }$ corresponds to the point $$\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$$ .
E) $t = \frac { 10 \pi } { 3 }$ corresponds to the point $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ .

Answer 2

$t = \frac { 10 \pi } { 3 }$ corresponds to the point $$\left( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$$ .

Question 3

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = \frac { 3 \pi } { 2 }$ ​

A) $t = \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } \sin \left( \frac { 3 \pi } { 2 } \right) = 0 \\\\\cos \left( \frac { 3 \pi } { 2 } \right) = - 1 \\\\\tan \left( \frac { 3 \pi } { 2 } \right) = 0\end{array}$
B) $t = \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ .​ $$\begin{array} { l } \sin \left( \frac { 3 \pi } { 2 } \right) = - 1 \\\\\cos \left( \frac { 3 \pi } { 2 } \right) = 0\\\\\tan \left( \frac { 3 \pi } { 2 } \right)~ is~ undefined.\end{array}$$ ​
C) $$t = \frac { 3 \pi } { 2 }$$ corresponds to the point $( x , y ) = ( 0,0 )$ .​ $$\begin{array} { l } \sin \left( \frac { 3 \pi } { 2 } \right) = 0 \\\\\cos \left( \frac { 3 \pi } { 2 } \right) = 0 \\\\\tan \left( \frac { 3 \pi } { 2 } \right) = 0\end{array}$$ ​
D) $t = \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ .​ $\begin{array} { l } \sin \left( \frac { 3 \pi } { 2 } \right) = - 1 \\\\\cos \left( \frac { 3 \pi } { 2 } \right) = 0 \\\\\tan \left( \frac { 3 \pi } { 2 } \right) = 0\end{array}$ ​
E)Not possible

Answer 3

$t = \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ .​ $$\begin{array} { l } \sin \left( \frac { 3 \pi } { 2 } \right) = - 1 \\\\\cos \left( \frac { 3 \pi } { 2 } \right) = 0\\\\\tan \left( \frac { 3 \pi } { 2 } \right)~ is~ undefined.\end{array}$$ ​

Question 4

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ a = $$\frac { 15 } { 17 }$$ ,b = $\frac { 8 } { 17 }$ ​

A)sin t = $\frac { 8 } { 17 }$ cos t = $$\frac { 8 } { 15 }$$
Tan t = $\frac { 15 } { 17 }$
B)​sin t = $\frac { 15 } { 17 }$ cos t = $\frac { 8 } { 17 }$
Tan t = $\frac { 8 } { 15 }$
C)​sin t = $\frac { 17 } { 15 }$ cos t = $\frac { 17 } { 8 }$
Tan t = $\frac { 15 } { 8 }$
D)sin t = $\frac { 8 } { 15 }$ cos t = $\frac { 15 } { 17 }$
Tan t = $\frac { 8 } { 17 }$
E)​sin t = $\frac { 8 } { 17 }$ cos t = $\frac { 15 } { 17 }$
Tan t = $\frac { 8 } { 15 }$

Question 5

Find the point (x,y)on the unit circle that corresponds to the real number t.(Round your answer to one decimal place. )​ $t = \frac { \pi } { 2 }$ ​

A) $t = \frac { \pi } { 2 }$ corresponds to the point $( 0.0 , - 1.0 )$ .
B) $t = \frac { \pi } { 2 }$ corresponds to the point $( - 0.0 , - 1.0 )$ .
C) $t = \frac { \pi } { 2 }$ corresponds to the point $( 0.0,1.0 )$ .
D) $t = \frac { \pi } { 2 }$ corresponds to the point $( 1.0 , - 0.0 )$ .
E) $t = \frac { \pi } { 2 }$ corresponds to the point $( 1.0,0.0 )$ .

Question 6

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ $$a = \frac { 5 } { 13 } , b = \frac { 12 } { 13 }$$ ​

A)​ $\begin{array} { l } \sin t = - \frac { 12 } { 13 } \\\\\cos t = \frac { 5 } { 13 } \\\\\tan t = \frac { 12 } { 5 }\end{array}$ ​
B)​ $\begin{array} { l } \sin t = \frac { 13 } { 5 } \\\\\cos t = \frac { 13 } { 12 } \\\\\tan t = \frac { 5 } { 12 }\end{array}$ ​
C) $\begin{array} { l } \sin t = \frac { 12 } { 13 } \\\\\cos t = \frac { 12 } { 5 } \\\\\tan t = \frac { 5 } { 13 }\end{array}$ ​
D)​ $\begin{array} { l } \sin t = \frac { 12 } { 5 } \\\\\cos t = \frac { 5 } { 13 } \\\\\tan t = \frac { 12 } { 13 }\end{array}$ ​
E)​ $\begin{array} { l } \sin t = - \frac { 12 } { 13 } \\\cos t = \frac { 5 } { 13 } \\\tan t = - \frac { 12 } { 5 }\end{array}$ ​

Question 7

Evaluate (if possible)the sine,cosec,and tangent of the real number.​ $t = - 8 \pi$ ​

A) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } \sin ( - 8 \pi ) = 0 \\\csc ( - 8 \pi ) \text { is undefined } \\\tan ( - 8 \pi ) = 0\end{array}$
B) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } \sin ( - 8 \pi ) = 0 \\\csc ( - 8 \pi ) = 0 \\\tan ( - 8 \pi ) \text { is undefined }\end{array}$
C) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } \sin ( - 8 \pi ) = 1 \\\csc ( - 8 \pi ) = 0 \\\tan ( - 8 \pi ) \text { is undefined }\end{array}$
D) $t = - 8 \pi$ corresponds to the point $( x , y ) = ( 0,1 )$ . $\begin{array} { l } \sin ( - 8 \pi ) = 1 \\\csc ( - 8 \pi ) = 0 \\\tan ( - 8 \pi ) \text { is undefined }\end{array}$
E)Not possible

Question 8

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = - \frac { \pi } { 2 }$ ​

A) $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } \sin \left( - \frac { \pi } { 2 } \right) = 0 \\\cos \left( - \frac { \pi } { 2 } \right) = 0 \\\tan \left( - \frac { \pi } { 2 } \right) = 0\end{array}$
B) $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } \sin \left( - \frac { \pi } { 2 } \right) = - 1 \\\cos \left( - \frac { \pi } { 2 } \right) = 0 \\\tan \left( - \frac { \pi } { 2 } \right) = 0\end{array}$
C) $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ . $\begin{array} { l } \sin \left( - \frac { \pi } { 2 } \right) = - 1 \\\cos \left( - \frac { \pi } { 2 } \right) = 0 \\\tan \left( - \frac { \pi } { 2 } \right) \text { is undefined }\end{array}$
D) $t = - \frac { \pi } { 2 }$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } \sin \left( - \frac { \pi } { 2 } \right) = 0 \\\cos \left( - \frac { \pi } { 2 } \right) = - 1 \\\tan \left( - \frac { \pi } { 2 } \right) = 0\end{array}$
E)Not possible

Question 9

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 5 \pi } { 6 }$ ​

A) $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ .
B) $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ .
C) $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .
D) $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .
E) $t = \frac { 5 \pi } { 6 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ .

Question 10

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = - 7 \pi$ ​

A) $t = - 7 \pi$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ . $$\begin{array} { l } \sin ( - 7 \pi ) = - 1 \\\cos ( - 7 \pi ) = 0\\\tan ( - 7 \pi ) ~is~ undefined.\end{array}$$
B) $t = - 7 \pi$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $$\begin{array} { l } \sin ( - 7 \pi ) = - 1 \\\cos ( - 7 \pi ) = 0\\\tan ( - 7 \pi) ~is~ undefined.\end{array}$$
C) $t = - 7 \pi$ corresponds to the point $( x , y ) = ( 0 , - 1 )$ . $$\begin{array} { l } \sin ( - 7 \pi ) = 0 \\\cos ( - 7 \pi ) = 0\\\tan ( - 7 \pi ) ~is~ undefined.\end{array}$$
D) $t = - 7 \pi$ corresponds to the point $( x , y ) = ( - 1,0 )$ . $\begin{array} { l } \sin ( - 7 \pi ) = 0 \\\cos ( - 7 \pi ) = - 1 \\\tan ( - 7 \pi ) = 0\end{array}$
E)Not possible

Question 11

Evaluate the trigonometric function using its period as an aid. ​
Cos 8π
​

A)cos 8π = -8
B)cos 8π = 0
C)cos 8π = 8
D)cos 8π = ∞
E)cos 8π = 1

Question 12

Evaluate the trigonometric function using its period as an aid.​ $\sin \frac { 3 \pi } { 4 }$ ​

A) $\sin \frac { 3 \pi } { 4 } = \infty$
B) $\sin \frac { 3 \pi } { 4 } = - \sqrt { 2 }$
C) $\sin \frac { 3 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
D) $\sin \frac { 3 \pi } { 4 } = \sqrt { 2 }$
E) $\sin \frac { 3 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$

Question 13

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ $a = \frac { 12 } { 13 } , b = \frac { 5 } { 13 }$ ​

A)​ $\begin{array} { l } \sin t = - \frac { 5 } { 13 } \\\\\cos t = - \frac { 12 } { 13 } \\\\\tan t = - \frac { 5 } { 12 }\end{array}$ ​
B)​ $\begin{array} { l } \sin t = \frac { 5 } { 13 } \\\\\cos t = \frac { 12 } { 13 } \\\\\tan t = \frac { 5 } { 12 }\end{array}$ ​
C) $\begin{array} { l } \sin t = \frac { 5 } { 13 } \\\\\\cos t = - \frac { 12 } { 13 } \\\\\tan t = - \frac { 5 } { 12 }\end{array}$ ​
D)​ $\begin{array} { l } \sin t = \frac { 5 } { 12 } \\\\\cos t = \frac { 5 } { 13 } \\\\\tan t = \frac { 12 } { 13 }\end{array}$ ​
E)​ $\begin{array} { l } \sin t = \frac { 5 } { 13 } \\\cos t = - \frac { 12 } { 13 } \\\tan t = \frac { 5 } { 12 }\end{array}$ ​

Question 14

Find the exact values of the three trigonometric functions sine,cosine,tangent of the real number t.​ ​ $$a = \frac { 4 } { 5 } , b = \frac { 3 } { 5 }$$ ​

A)​ $\begin{array} { l } \sin t = - \frac { 3 } { 5 } \\\\\cos t = - \frac { 4 } { 5 } \\\\\tan t = - \frac { 3 } { 4 }\end{array}$ ​
B)​ $\begin{array} { l } \sin t = \frac { 3 } { 5 } \\\cos t = - \frac { 3 } { 4 } \\\tan t = \frac { 4 } { 5 }\end{array}$ ​
C) $\begin{array} { l } \sin t = - \frac { 3 } { 5 } \\\\\cos t = - \frac { 3 } { 4 } \\\\\tan t = \frac { 4 } { 5 }\end{array}$ ​
D)​ $\begin{array} { l } \sin t = \frac { 3 } { 4 } \\\\\cos t = \frac { 3 } { 5 } \\\\\tan t = \frac { 4 } { 5 }\end{array}$ ​
E)​ $\begin{array} { l } \sin t = - \frac { 3 } { 5 } \\\\\cos t = - \frac { 4 } { 5 } \\\\\tan t = \frac { 3 } { 4 }\end{array}$ ​

Question 15

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = - \frac { 3 \pi } { 2 }$ ​

A) $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 0,0 )$ . $\begin{array} { l } \sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\\\\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\\\\tan \left( - \frac { 3 \pi } { 2 } \right) = 0\end{array}$
B) $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ . $\begin{array} { l } \sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\\\\cos \left( - \frac { 3 \pi } { 2 } \right) = 0 \\\\\tan \left( - \frac { 3 \pi } { 2 } \right) = 0\end{array}$
C) $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $$( x , y ) = ( 0,1 )$$ . $$\begin{array} { l } \sin \left( - \frac { 3 \pi } { 2 } \right) = 1 \\\\\cos \left( - \frac { 3 \pi } { 2 } \right) = 0\\\\\tan \left( - \frac { 3 \pi } { 2 } \right)~ is~ undefined.\end{array}$$
D) $t = - \frac { 3 \pi } { 2 }$ corresponds to the point $( x , y ) = ( 1,0 )$ .​ $\begin{array} { l } \sin \left( - \frac { 3 \pi } { 2 } \right) = 0 \\\\\cos \left( - \frac { 3 \pi } { 2 } \right) = 1 \\\\\tan \left( - \frac { 3 \pi } { 2 } \right) = 0\end{array}$ ​
E)Not possible

Question 16

Evaluate the trigonometric function using its period as an aid.​ $\sin 4 \pi$ ​

A) $\sin 4 \pi = 4$
B) $\sin 4 \pi = - 1$
C) $\sin 4 \pi = - 4$
D) $\sin 4 \pi = 0$
E) $\sin 4 \pi = \infty$

Question 17

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = \frac { 19 \pi } { 3 }$ ​

A) $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ .
B) $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .
C) $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ .
D) $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ .
E) $t = \frac { 19 \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ .

Question 18

Evaluate the trigonometric function using its period as an aid.​ $\cos \frac { 5 \pi } { 3 }$ ​

A) $\cos \frac { 5 \pi } { 3 } = \infty$
B) $\cos \frac { 5 \pi } { 3 } = - \frac { 1 } { 2 }$
C) $\cos \frac { 5 \pi } { 3 } = 2$
D) $\cos \frac { 5 \pi } { 3 } = - 2$
E) $\cos \frac { 5 \pi } { 3 } = \frac { 1 } { 2 }$

Question 19

Evaluate (if possible)the sine,cosine,and tangent of the real number.​ $t = \frac { 9 \pi } { 4 }$ ​

A) $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \\\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \\\tan \left( \frac { 9 \pi } { 4 } \right) = - 1\end{array}$
B) $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \\\cos \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \\\tan \left( \frac { 9 \pi } { 4 } \right) = 1\end{array}$ ​
C) $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , - \frac { \sqrt { 2 } } { 2 } \right)$ . $\begin{array} { l } \sin \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \\\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \\\tan \left( \frac { 9 \pi } { 4 } \right) = 1\end{array}$ ​
D) $t = \frac { 9 \pi } { 4 }$ corresponds to the point $( x , y ) = \left( - \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ .​ $\begin{array} { l } \sin \left( \frac { 9 \pi } { 4 } \right) = \frac { \sqrt { 2 } } { 2 } \\\cos \left( \frac { 9 \pi } { 4 } \right) = - \frac { \sqrt { 2 } } { 2 } \\\tan \left( \frac { 9 \pi } { 4 } \right) = - 1\end{array}$
E)Not possible

Question 20

Find the point (x,y)on the unit circle that corresponds to the real number t.​ $t = 3 \pi$ ​

A) $t = 3 \pi$ corresponds to the point $( - 1,0 )$ .
B) $t = 3 \pi$ corresponds to the point $( 0 , - 1 )$ .
C) $t = 3 \pi$ corresponds to the point $( 0,3 )$ .
D) $t = 3 \pi$ corresponds to the point $( 3,0 )$ .
E) $t = 3 \pi$ corresponds to the point $( - 1 , - 1 )$ .

Question 21

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\sin \frac { \pi } { 6 }$ ​

A) $\sin \frac { \pi } { 6 } \approx$ - 0.5000
B) $\sin \frac { \pi } { 6 } \approx$ 0.6000
C) $\sin \frac { \pi } { 6 } \approx$ 0.4000
D) $\sin \frac { \pi } { 6 } \approx$ 0.7000
E) $\sin \frac { \pi } { 6 } \approx$ 0.5000

Question 22

Use the value of the trigonometric function to find $\csc ( - t )$ .​ $\sin t = \frac { 1 } { 6 }$ ​

A) $\csc ( - t ) = \frac { 1 } { 6 }$
B) $\csc ( - t ) = 6$
C) $\csc ( - t ) = - \frac { 1 } { 6 }$
D) $\csc ( - t ) = - 6$
E) $\csc ( - t ) = \infty$

Question 23

Use the value of the trigonometric function to find $\sec ( - t )$ .​ $\cos ( - t ) = - \frac { 1 } { 6 }$ ​

A) $\sec ( - t ) = \infty$
B) $\sec ( - t ) = - \frac { 1 } { 6 }$
C) $\sec ( - t ) = - 6$
D) $\sec ( - t ) = \frac { 1 } { 6 }$
E) $\sec ( - t ) = 6$

Question 24

Use the value of the trigonometric function to find $\cos ( \pi - t )$ .​ $\cos t = \frac { 5 } { 6 }$ ​

A) $\cos ( \pi - t ) = \frac { 5 } { 6 }$
B) $\cos ( \pi - t ) = - \frac { 5 } { 6 }$
C) $\cos ( \pi - t ) = \frac { 6 } { 5 }$
D) $\cos ( \pi - t ) = \infty$
E) $\cos ( \pi - t ) = - \frac { 6 } { 5 }$

Question 25

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cot \frac { \pi } { 7 }$ ​

A) $\cot \frac { \pi } { 7 } \approx 2.0765$
B) $\cot \frac { \pi } { 7 } \approx 1.9765$
C) $\cot \frac { \pi } { 7 } \approx 2.2765$
D) $\cot \frac { \pi } { 7 } \approx - 2.0765$
E) $\cot \frac { \pi } { 7 } \approx 2.1765$

Question 26

Use the value of the trigonometric function to find $\sin t$ .​ $\sin ( - t ) = \frac { 3 } { 10 }$ ​

A) $\sin t = \frac { 10 } { 3 }$
B) $\sin t = \frac { 3 } { 10 }$
C) $\sin t = \infty$
D) $\sin t = - \frac { 3 } { 10 }$
E) $$\sin t = - \frac { 10 } { 3 }$$

Question 27

Use the value of the trigonometric function to find $\sin ( \pi - t )$ .​ $\sin t = \frac { 6 } { 7 }$ ​

A) $\sin ( \pi - t ) = \frac { 6 } { 7 }$
B) $\sin ( \pi - t ) = - \frac { 6 } { 7 }$
C) $\sin ( \pi - t ) = - \frac { 7 } { 6 }$
D) $\sin ( \pi - t ) = \infty$
E) $\sin ( \pi - t ) = \frac { 7 } { 6 }$

Question 28

Evaluate the trigonometric function using its period as an aid.​ $\cos \frac { 23 \pi } { 4 }$ ​

A) $\cos \frac { 23 \pi } { 4 } = - \frac { \sqrt { 2 } } { 2 }$
B) $\cos \frac { 23 \pi } { 4 } = - \sqrt { 2 }$
C) $\cos \frac { 23 \pi } { 4 } = \sqrt { 2 }$
D) $\cos \frac { 23 \pi } { 4 } = \frac { \sqrt { 2 } } { 2 }$
E) $\cos \frac { 23 \pi } { 4 } = \infty$

Question 29

Find the value of given trigonometric function.Round your answer to four decimal places..​ $$\csc \frac { 2 \pi } { 3 }$$ ​

A) $\csc \frac { 2 \pi } { 3 } \approx 1.1547$
B) $\csc \frac { 2 \pi } { 3 } \approx 1.2547$
C) $\csc \frac { 2 \pi } { 3 } \approx - 1.1547$
D) $\csc \frac { 2 \pi } { 3 } \approx 1.0547$
E) $\csc \frac { 2 \pi } { 3 } \approx 1.3547$

Question 30

Use the value of the trigonometric function to find $\cos ( - t )$ .​ $\cos t = - \frac { 3 } { 8 }$ ​

A) $\cos ( - t ) = \frac { 8 } { 3 }$
B) $\cos ( - t ) = \frac { 3 } { 8 }$
C) $\cos ( - t ) = - \frac { 3 } { 8 }$
D) $\cos ( - t ) = - \frac { 8 } { 3 }$
E) $\cos ( - t ) = \infty$

Question 31

Use the value of the trigonometric function to find $\sec ( - t )$ .​ $\cos t = - \frac { 3 } { 4 }$ ​

A) $\sec ( - t ) = \frac { 4 } { 3 }$
B) $\sec ( - t ) = - \frac { 3 } { 4 }$
C) $\sec ( - t ) = - \frac { 4 } { 3 }$
D) $\sec ( - t ) = \infty$
E) $\sec ( - t ) = \frac { 3 } { 4 }$

Question 32

Use the value of the trigonometric function to find the $\sin ( - t )$ .​ $\sin t = \frac { 1 } { 6 }$ ​

A) $\sin ( - t ) = - \frac { 1 } { 6 }$
B) $\sin ( - t ) = - 6$
C) $\sin ( - t ) = 6$
D) $\sin ( - t ) = \infty$
E) $\sin ( - t ) = \frac { 1 } { 6 }$

Question 33

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cos ( - 2.5 )$ ​

A) $\cos ( - 2.5 ) \approx - 0.7011$
B) $\cos ( - 2.5 ) \approx 0.8011$
C) $\cos ( - 2.5 ) \approx - 0.8011$
D) $\cos ( - 2.5 ) \approx - 0.9011$
E) $\cos ( - 2.5 ) \approx - 0.6011$

Question 34

Use the value of the trigonometric function to find $\sin ( t + \pi )$ .​ $\sin t = \frac { 7 } { 8 }$ ​

A) $\sin ( t + \pi ) = - \frac { 8 } { 7 }$
B) $\sin ( t + \pi ) = \frac { 8 } { 7 }$
C) $\sin ( t + \pi ) = \frac { 7 } { 8 }$
D) $\sin ( t + \pi ) = \infty$
E) $\sin ( t + \pi ) = - \frac { 7 } { 8 }$

Question 35

Use the value of the trigonometric function to find $\cos~ t$ .​ $\cos ( - t ) = - \frac { 1 } { 4 }$ ​

A) $\cos t = \frac { 1 } { 4 }$
B) $\cos t = - 4$
C) $\cos t = \infty$
D) $\cos t = 4$
E) $\cos t = - \frac { 1 } { 4 }$

Question 36

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cos ( - 1.6 )$ ​

A) $\cos ( - 1.6 ) \approx 0.1708$
B) $\cos ( - 1.6 ) \approx 0.0708$
C) $\cos ( - 1.6 ) \approx 0.0292$
D) $\cos ( - 1.6 ) \approx - 0.0292$
E) $\cos ( - 1.6 ) \approx - 0.1292$

Question 37

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\tan \frac { \pi } { 8 }$ ​

A) $\tan \frac { \pi } { 8 } \approx$ 0.3142
B) $\tan \frac { \pi } { 8 } \approx$ 0.6142
C) $\tan \frac { \pi } { 8 } \approx$ - 0.4142
D) $\tan \frac { \pi } { 8 } \approx$ 0.4142
E) $\tan \frac { \pi } { 8 } \approx$ 0.5142

Question 38

Use the value of the trigonometric function to find $\csc t$ .​ $\sin ( - t ) = \frac { 3 } { 4 }$ ​

A) $\csc t = \frac { 3 } { 4 }$
B) $\csc t = - \frac { 3 } { 4 }$
C) $\csc t = \infty$
D) $\csc t = \frac { 4 } { 3 }$
E) $\csc t = - \frac { 4 } { 3 }$

Question 39

Use the value of the trigonometric function to find $\cos ( t + \pi )$ .​ $\cos t = \frac { 7 } { 8 }$ ​

A) $\cos ( t + \pi ) = \frac { 7 } { 8 }$
B) $\cos ( t + \pi ) = - \frac { 8 } { 7 }$
C) $\cos ( t + \pi ) = \infty$
D) $\cos ( t + \pi ) = \frac { 8 } { 7 }$
E) $\cos ( t + \pi ) = - \frac { 7 } { 8 }$

Question 40

Evaluate the trigonometric function using its period as an aid.​ $\sin \left( \frac { 11 \pi } { 6 } \right)$ ​

A) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { 1 } { 2 }$
B) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { \sqrt { 2 } } { 2 }$
C) $\sin \left( \frac { 11 \pi } { 6 } \right) = \infty$
D) $\sin \left( \frac { 11 \pi } { 6 } \right) = \frac { 1 } { 2 }$
E) $\sin \left( \frac { 11 \pi } { 6 } \right) = - \frac { \sqrt { 2 } } { 2 }$

Question 41

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\cot ( - 0.9 )$ ​

A) $\cot ( - 0.9 ) \approx - 0.6936$
B) $\cot ( - 0.9 ) \approx - 0.7936$
C) $\cot ( - 0.9 ) \approx - 0.5936$
D) $\cot ( - 0.9 ) \approx - 0.8936$
E) $\cot ( - 0.9 ) \approx 0.7936$

Question 42

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\csc~ 0.5$ ​

A) $\csc 0.5 \approx 2.2858$
B) $\csc 0.5 \approx - 2.0858$
C) $\csc 0.5 \approx 2.0858$
D) $\csc 0.5 \approx 1.9858$
E) $\csc~ 0.5 \approx 2.1858$

Question 43

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by $y ( t ) = \frac { 1 } { 4 } e ^ { - t } \cos 6 t$ ,where y is the displacement (in feet)and t is the time (in seconds).Complete the following table.(Round your answer to four decimal places. ) ​
$$\begin{array} { | c | c | c | c | c | c | } \hline\\ t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\\\\hline y & & & & & \\\hline\end{array}$$

A) $\begin{array}{|l|l|l|l|l|l|}\hline \\t&1 & \frac{1}{8} & \frac{1}{5} & \frac{3}{7} & 5\\\\\hline y & 0.0883 & 0.1614 & 0.0742 & 0.0629 & 0.2003\\\hline\end{array}$
B) $$\begin{array} { | c | c | c | c | c | c | } \hline \\t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\\\\hline y & 0.0883 & 0.1614 & 0.2742 & - 0.1371 & 0.0003 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } \hline \\t & 1 & \frac { 1 } { 8 } & \frac { 1 } { 5 } & \frac { 3 } { 7 } & 5 \\\\\hline y & 0.1883 & 0.3614 & 0.0742 & - 0.1371 & 0.0883 \\\hline\end{array}$$

Question 44

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\sec ( - 22.3 )$ ​

A) $\sec ( - 22.3 ) \approx - 0.8497$
B) $\sec ( - 22.3 ) \approx 1.0497$
C) $\sec ( - 22.3 ) \approx - 0.9497$
D) $\sec ( - 22.3 ) \approx - 1.1497$
E) $\sec ( - 22.3 ) \approx - 1.0497$

Question 45

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos ( 6 t )$ ,where y is the displacement (in feet)and t is the time (in seconds).Find the displacements when $t = 5$ .(Round your answers to two decimal places. )
​

A) $y ( 5 ) \approx 0.04$ foot
B) $y ( 5 ) \approx 0.14$ foot
C) $y ( 5 ) \approx 0.44$ foot
D) $y ( 5 ) \approx 0.34$ foot
E) $y ( 5 ) \approx 0.24$ foot

Question 46

Find the point $( x , y )$ on the unit circle that corresponds to the real number $\frac { 5 \pi } { 6 }$ .Use your results to evaluate $\cos t$ .

A) $\cos t = \frac { \sqrt { 3 } } { 2 }$
B) $\cos t = - \frac { \sqrt { 3 } } { 2 }$
C) $\cos t = - \frac { 1 } { 2 }$
D) $\cos t = - 1$
E) $\cos t = 1$

Question 47

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos 6 t$ ,where y is the displacement (in feet)and t is the time (in seconds).Find the displacements when $t = \frac { 1 } { 2 }$ .
​

A) $y \left( \frac { 1 } { 2 } \right) \approx - 0.15$ foot
B) $y \left( \frac { 1 } { 2 } \right) \approx 0.15$ foot
C) $y \left( \frac { 1 } { 2 } \right) \approx - 0.05$ foot
D) $y \left( \frac { 1 } { 2 } \right) \approx 0.05$ foot
E) $y \left( \frac { 1 } { 2 } \right) \approx - 0.25$ foot

Question 48

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\text { sec } 1.6$ ​

A) $\sec 1.6 \approx - 34.1471$
B) $\sec 1.6 \approx - 34.0471$
C) $\sec 1.6 \approx - 34.2471$
D) $\sec 1.6 \approx - 34.3471$
E) $\sec 1.6 \approx 34.2471$

Question 49

Find the point $( x , y )$ on the unit circle that corresponds to the real number $t = \frac { 5 \pi } { 4 }$ .Use your results to evaluate $\tan t$ .

A) $\tan t = \frac { \sqrt { 2 } } { 2 }$
B) $\tan t = 0$
C) $\tan t = - \frac { \sqrt { 2 } } { 2 }$
D) $\tan t = 1$
E) $\tan t = \text { undefined }$

Question 50

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = 3 \cos 10 t$ ,where y is the displacement in centimeters and t is the time in seconds.Find the displacement when $t = 0.65$ ,rounding answer to four decimal places.

A)-3.7018 cm
B)-6.4350 cm
C)23.8825 cm
D)2.9298 cm
E)-1.6362 cm