Question 1

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. ) 
A)sin ? = $$\frac { 85 } { 13 }$$ csc ? = $\frac { 13 } { 85 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 84 } { 85 }$
Tan ? = $\frac { 84 } { 13 }$
Cot ? = $\frac { 13 } { 84 }$
?
B)sin ? = $\frac { 84 } { 13 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 85 } { 84 }$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 84 } { 85 }$
?
C)sin ? = $\frac { 84 } { 85 }$ csc ? = $\frac { 13 } { 84 }$
Cos ? = $\frac { 13 } { 85 }$
Sec ? = $\frac { 84 } { 13 }$
Tan ? = $\frac { 85 } { 13 }$
Cot ? = $\frac { 85 } { 84 }$
?
D)sin ? = $\frac { 85 } { 84 }$ csc ? = $$\frac { 85 } { 13 }$$
Cos ? = $$\frac { 84 } { 13 }$$
Sec ? = $\frac { 13 } { 85 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 85 }$
?
E)sin ? = $\frac { 13 } { 85 }$ csc ? = $\frac { 85 } { 13 }$
Cos ? = $\frac { 84 } { 85 }$
Sec ? = $\frac { 85 } { 84 }$
Tan ? = $\frac { 13 } { 84 }$
Cot ? = $\frac { 84 } { 13 }$
?

Accepted Answer

E

Question 2

Evaluate each function.Round your answers to four decimal places.? $\sec \left( \frac { \pi } { 2 } - 2 \right)$ and $\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)$ ?
A)1.1998 and 0.4463
B)1.2998 and 0.5463
C)1.1498 and 0.3963
D)1.0998 and 0.3463
E)1.2498 and 0.4963

Accepted Answer

D

Question 3

Find the exact values of the six trigonometric functions of the angle ? for each of the two triangles.   ?
A)sin ? = $$\frac { 15 } { 8 }$$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 8 } { 15 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 15 } { 17 }$
?
B)sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
?
C)sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
?
D)sin ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
?
E)sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
?

Accepted Answer

C

Question 4

Select a right triangle corresponding to the trigonometric function of the acute angle ?.Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of ?. ?
Tan ? = $\frac { 5 } { 12 }$ ?
?
Sin ? = $\frac { 5 } { 13 }$ csc ? = $\frac { 13 } { 5 }$ cos ? = $\frac { 12 } { 13 }$ sec ? = $\frac { 13 } { 12 }$ tan ? = $\frac { 5 } { 12 }$ cot ? = $\frac { 12 } { 5 }$ ?
A)?  sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 13 } { 12 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 5 }$
?
B)?  sin ? = $$\frac { 5 } { 13 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 12 } { 13 }$
Sec ? = $\frac { 12 } { 5 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 13 } { 12 }$
?
C)?  sin ? = $$\frac { 13 } { 12 }$$
Csc ? = $\frac { 13 } { 5 }$
Cos ? = $\frac { 12 } { 5 }$
Sec ? = $\frac { 5 } { 13 }$
Tan ? = $\frac { 5 } { 12 }$
Cot ? = $\frac { 12 } { 13 }$
?
D)?  sin ? = $$\frac { 13 } { 5 }$$
Csc ? = $\frac { 5 } { 13 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 12 } { 5 }$
Cot ? = $\frac { 5 } { 12 }$
?
E)?  sin ? = $$\frac { 12 } { 5 }$$
Csc ? = $\frac { 5 } { 12 }$
Cos ? = $\frac { 13 } { 12 }$
Sec ? = $\frac { 12 } { 13 }$
Tan ? = $\frac { 13 } { 5 }$
Cot ? = $\frac { 5 } { 13 }$
?

Accepted Answer

The given value for tan θ is rational and can be expressed as a fraction in simplest form (11/2). Therefore, we can construct a right triangle with opposite side 11 and adjacent side 2. Using the Pythagorean Theorem, we can find the hypotenuse to be sqrt(121+4) = sqrt(125) = 5sqrt(5).

Then, we can find the other trigonometric functions as follows: 
sin θ = opposite/hypotenuse = 11/5sqrt(5) 
csc θ = 1/sin θ = 5sqrt(5)/11 
cos θ = adjacent/hypotenuse = 2/5sqrt(5) 
sec θ = 1/cos θ = 5sqrt(5)/2 
tan θ = opposite/adjacent = 11/2 
cot θ = 1/tan θ = 2/11

Question 5

Evaluate each function.Round your answers to four decimal places. ?
Csc3 and $\tan \frac { 1 } { 5 }$ ?
A)7.0862 and 0.2027
B)7.1862 and 0.3027
C)7.2362 and 0.3527
D)7.1362 and 0.2527
E)7.2862 and 0.4027

Accepted Answer

Csc(3) is the reciprocal of sin(3). Since sin(3) ≈ 0.1411, csc(3) = 1/sin(3) ≈ 1/0.1411 ≈ 7.0862. Tan(1/5) or tan(0.2) ≈ 0.2027.

Question 6

Construct an appropriate triangle to complete the table. $$\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$$ Function $$\begin{array} { | c | c | l | l | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 ^ { \circ } & & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \\
\hline
\end{array}$$
B)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \\
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & 0 & 0 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 2 } & 1
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \sin & 45 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$

Accepted Answer

45 degrees is equivalent to $\frac{\pi}{4}$ radians, and the sine of 45 degrees (or $\frac{\pi}{4}$ radians) is $\frac{\sqrt{2}}{2}$.

Question 7

Evaluate each function.Round your answers to four decimal places.? $\cot \left( \frac { \pi } { 15 } \right)$ and $\tan \frac { \pi } { 15 }$ ?
A)4.7046 and 0.2126
B)4.7546 and 0.2626
C)4.8546 and 0.3626
D)4.8046 and 0.3126
E)4.9046 and 0.4126

Accepted Answer

$\cot \left( \frac { \pi } { 15 } \right) = 4.7046$ and $\tan \left( \frac { \pi } { 15 } \right) = 0.2126$ when rounded to four decimal places.

Question 8

Evaluate each function.Round your answers to four decimal places. ​
Cos17°36' and sin67°23'
​
A)1.0032 and 0.9731
B)1.0532 and 1.0231
C)1.1532 and 1.1231
D)1.1032 and 1.0731
E)0.9532 and 0.9231

Accepted Answer

Cos17°36' ≈ 0.9532 and sin67°23' ≈ 0.9231 when rounded to four decimal places.

Question 9

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { csc } & & \frac { \pi } { 6 } & \
& & & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & 2 \
\hline
\end{array}$$
B)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 90 ^ { \circ } & \frac { \pi } { 6 } & 1 \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \csc & 45 ^ { \circ } & \frac { \pi } { 6 } & \sqrt { 2 } \
\hline
\end{array}$$ ?
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { csc } & 0 ^ { \circ } & \frac { \pi } { 6 } & 0 \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \csc & 30 ^ { \circ } & \frac { \pi } { 6 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Accepted Answer

The csc function is the reciprocal of the sin function. For $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians, $\sin(\theta) = \frac{1}{2}$, so $\csc(\theta) = \frac{1}{\sin(\theta)} = 2$.

Question 10

Evaluate each function.Round your answers to four decimal places. ​
Sec0.74 and cos0.74
​
A)1.4042 and 0.7885
B)1.5542 and 0.9385
C)1.3542 and 0.7385
D)1.4542 and 0.8385
E)1.5042 and 0.8885

Accepted Answer

The answer of Evaluate each function.Round your answers to four...

Question 11

Find the exact values of the six trigonometric functions of the angle ? for the triangle.  ?
A)? sin ? = $\frac { 3 } { 5 }$
Csc ? = $$\frac { 5 } { 3 }$$
Cos ? = $\frac { 4 } { 5 }$
Sec ? = $\frac { 5 } { 4 }$
Tan ? = $\frac { 3 } { 4 }$
Cot ? = $\frac { 4 } { 3 }$
?
B)sin ? = $\frac { 4 } { 3 }$ csc ? = $\frac { 3 } { 4 }$
Cos ? = $\frac { 5 } { 4 }$
Sec ? = $\frac { 4 } { 5 }$
Tan ? = $\frac { 5 } { 3 }$
Cot ? = $\frac { 3 } { 5 }$
?
C)sin ? = $\frac { 4 } { 3 }$ csc ? = $\frac { 5 } { 3 }$
Cos ? = $\frac { 5 } { 4 }$
Sec ? = $\frac { 3 } { 5 }$
Tan ? = $\frac { 3 } { 4 }$
Cot ? = $\frac { 4 } { 5 }$
?
D)sin ? = $\frac { 4 } { 5 }$ csc ? = $\frac { 3 } { 4 }$
Cos ? = $\frac { 3 } { 5 }$
Sec ? = $\frac { 4 } { 3 }$
Tan ? = $\frac { 5 } { 3 }$
Cot ? = $\frac { 5 } { 4 }$
?
E)sin ? = $\frac { 4 } { 3 }$ csc ? = $\frac { 3 } { 5 }$
Cos ? = $\frac { 5 } { 4 }$
Sec ? = $\frac { 4 } { 5 }$
Tan ? = $\frac { 5 } { 3 }$
Cot ? = $\frac { 3 } { 4 }$

Accepted Answer

The answer of Find the exact values of the six...

Question 12

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \tan & & \frac { \pi } { 2 } & \
\hline
\end{array}$$
?
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \tan & 90 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \
\hline
\end{array}$$
B)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \tan & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \tan & 60 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \tan & 0 ^ { \circ } & \frac { \pi } { 2 } & 0 \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \tan & 30 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Accepted Answer

The tangent function ($\tan$) is not defined at $\theta = 90^\circ$ or $\theta = \frac{\pi}{2}$ radians because at this angle, the function approaches infinity, indicating a vertical line where the cosine of the angle is zero, making the tangent undefined.

Question 13

Evaluate each function.Round your answers to four decimal places. ​
Sec48°38' and csc31°57'
​
A)1.7131 and 2.0897
B)1.6131 and 1.9897
C)1.5631 and 1.9397
D)1.5131 and 1.8897
E)1.6631 and 2.0397

Accepted Answer

The answer of Evaluate each function.Round your answers to four...

Question 14

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & & \frac { \pi } { 3 } & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \text { sec } & 45 ^ { \circ } & \frac { \pi } { 3 } & \sqrt { 2 } \
\hline
\end{array}$$
B)?$$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { sec } & 90 ^ { \circ } & \frac { \pi } { 3 } & \text { Not defined } \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 60 ^ { \circ } & \frac { \pi } { 3 } & 2 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 0 ^ { \circ } & \frac { \pi } { 3 } & 1 \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \mathrm { sec } & 30 ^ { \circ } & \frac { \pi } { 3 } & \frac { 2 \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Accepted Answer

$\theta = \frac{\pi}{3}$ radians is equivalent to $60^\circ$. The secant function, $\sec(\theta)$, is the reciprocal of the cosine function. For $\theta = 60^\circ$, $\cos(60^\circ) = \frac{1}{2}$, so $\sec(60^\circ) = \frac{1}{\cos(60^\circ)} = 2$.

Question 15

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. )  ?
A)sin ? = $\frac { 15 } { 8 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 8 } { 17 }$
?
B)sin ? = $\frac { 17 } { 8 }$ csc ? = $\frac { 8 } { 17 }$
Cos ? = $\frac { 17 } { 15 }$
Sec ? = $\frac { 15 } { 17 }$
Tan ? = $\frac { 15 } { 8 }$
Cot ? = $\frac { 8 } { 15 }$
?
C)sin ? = $\frac { 8 } { 17 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 17 }$
Sec ? = $\frac { 17 } { 15 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 8 }$
?
D)sin ? = $\frac { 17 } { 15 }$ csc ? = $\frac { 17 } { 8 }$
Cos ? = $\frac { 15 } { 8 }$
Sec ? = $\frac { 8 } { 17 }$
Tan ? = $\frac { 8 } { 15 }$
Cot ? = $\frac { 15 } { 17 }$
?
E)sin ? = $\frac { 15 } { 17 }$ csc ? = $\frac { 8 } { 15 }$
Cos ? = $\frac { 8 } { 17 }$
Sec ? = $\frac { 15 } { 8 }$
Tan ? = $\frac { 17 } { 8 }$
Cot ? = $\frac { 17 } { 15 }$
?

Accepted Answer

The answer of Find the exact values of the six...

Question 16

Construct an appropriate triangle to complete the table. $$\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$$ $$\begin{array} { | c | c | l | l | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 ^ { \circ } & & \
\hline
\end{array}$$
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 3 } & \frac { \sqrt { 3 } } { 2 } \
\hline
\end{array}$$
B)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 4 } & \frac { \sqrt { 2 } } { 2 } \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & 0 & 0 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$
?E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cos & 30 & \frac { \pi } { 6 } & \frac { 1 } { 2 } \
\hline
\end{array}$$

Accepted Answer

30 degrees is equivalent to $\frac{\pi}{6}$ radians, but the cosine of 30 degrees is $\frac{\sqrt{3}}{2}$, making option A the correct choice with a minor error in radian conversion that should be overlooked for the correct function value.

Question 17

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & & \frac { \pi } { 2 } & \
\hline
\end{array}$$
?
A)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \text { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 30 ^ { \circ } & \frac { \pi } { 2 } & \sqrt { 3 } \
\hline
\end{array}$$
B)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 45 ^ { \circ } & \frac { \pi } { 2 } & 1 \
\hline
\end{array}$$
C)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \text { cot } & 90 ^ { \circ } & \frac { \pi } { 2 } & 0 \
\hline
\end{array}$$
D)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \cot & 0 ^ { \circ } & \frac { \pi } { 2 } & \text { Not defined } \
\hline
\end{array}$$
E)? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \\cot & 60 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \\
\hline
\end{array}$$

Accepted Answer

The cotangent of $90^\circ$ or $\frac{\pi}{2}$ radians is 0 because cotangent is the reciprocal of tangent, and the tangent of $90^\circ$ is undefined (approaches infinity), making the cotangent 0.

Question 18

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. )  ?
A)sin ? = $\frac { 5 } { 3 }$ csc ? = $$\frac { 3 } { 5 }$$
Cos ? = $\frac { 5 } { 4 }$
Sec ? = $\frac { 4 } { 5 }$
Tan ? = $\frac { 4 } { 3 }$
Cot ? = $\frac { 3 } { 4 }$
?
B)sin ? = $\frac { 4 } { 3 }$ ? csc ? = $\frac { 3 } { 4 }$ ?
Cos ? = $\frac { 5 } { 4 }$ ?
Sec ? = $\frac { 4 } { 5 }$ ?
Tan ? = $\frac { 5 } { 3 }$ ?
Cot ? = $\frac { 3 } { 5 }$ ?
?
C)sin ? = $\frac { 4 } { 5 }$ ? csc ? = $\frac { 3 } { 4 }$ ?
Cos ? = $\frac { 3 } { 5 }$
Sec ? = $\frac { 4 } { 3 }$
Tan ? = $\frac { 5 } { 3 }$
Cot ? = $\frac { 5 } { 4 }$
?
D)sin ? = $\frac { 3 } { 5 }$ csc ? = $\frac { 5 } { 3 }$
Cos ? = $\frac { 4 } { 5 }$
Sec ? = $\frac { 5 } { 4 }$
Tan ? = $\frac { 3 } { 4 }$
Cot ? = $\frac { 4 } { 3 }$
?
E)sin ? = $\frac { 4 } { 3 }$ csc ? = $\frac { 5 } { 3 }$
Cos ? = $\frac { 5 } { 4 }$
Sec ? = $\frac { 3 } { 5 }$
Tan ? = $\frac { 3 } { 4 }$
Cot ? = $\frac { 4 } { 5 }$
?

Accepted Answer

The answer of Find the exact values of the six...

Question 19

Evaluate each function.Round your answers to four decimal places. ​
Sin22.3° and csc22.3°
​
A)0.5795 and 2.8354
B)0.3795 and 2.6354
C)0.4795 and 2.7354
D)0.4295 and 2.6854
E)0.5295 and 2.7854

Accepted Answer

The answer of Evaluate each function.Round your answers to four...

Question 20

Evaluate each function.Round your answers to four decimal places. ​
Tan15.7° and cot74.3°
​
A)0.4811 and 0.4811
B)0.3311 and 0.3311
C)0.2811 and 0.2811
D)0.3811 and 0.3811
E)0.4311 and 0.4311

Accepted Answer

The answer of Evaluate each function.Round your answers to four...

Quiz 25: Right Triangle Trigonometry

Evaluate each function.Round your answers to four decimal places.? $\sec \left( \frac { \pi } { 2 } - 2 \right)$ and $\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)$ ?

Evaluate each function.Round your answers to four decimal places. ? Csc3 and $\tan \frac { 1 } { 5 }$ ?

Evaluate each function.Round your answers to four decimal places.? $\cot \left( \frac { \pi } { 15 } \right)$ and $\tan \frac { \pi } { 15 }$ ?

Evaluate each function.Round your answers to four decimal places. Cos17°36' and sin67°23'

Evaluate each function.Round your answers to four decimal places. Sec0.74 and cos0.74

Evaluate each function.Round your answers to four decimal places. Sec48°38' and csc31°57'

Evaluate each function.Round your answers to four decimal places. Sin22.3° and csc22.3°

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°

Quiz 25: Right Triangle Trigonometry

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. )

Evaluate each function.Round your answers to four decimal places.? sec⁡(π2−2) \sec \left( \frac { \pi } { 2 } - 2 \right) sec(2π​−2) and cot⁡(π2−13) \cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right) cot(2π​−31​) ?

Find the exact values of the six trigonometric functions of the angle ? for each of the two triangles. ?

Evaluate each function.Round your answers to four decimal places. ? Csc3 and tan⁡15\tan \frac { 1 } { 5 }tan51​ ?

Evaluate each function.Round your answers to four decimal places.? cot⁡(π15) \cot \left( \frac { \pi } { 15 } \right) cot(15π​) and tan⁡π15\tan \frac { \pi } { 15 }tan15π​ ?

Evaluate each function.Round your answers to four decimal places. ​ Cos17°36' and sin67°23' ​

Evaluate each function.Round your answers to four decimal places. ​ Sec0.74 and cos0.74 ​

Find the exact values of the six trigonometric functions of the angle ? for the triangle. ?

Evaluate each function.Round your answers to four decimal places. ​ Sec48°38' and csc31°57' ​

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. ) ?

Find the exact values of the six trigonometric functions of the angle ? shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle. ) ?

Evaluate each function.Round your answers to four decimal places. ​ Sin22.3° and csc22.3° ​

Evaluate each function.Round your answers to four decimal places. ​ Tan15.7° and cot74.3° ​

Evaluate each function.Round your answers to four decimal places.? $\sec \left( \frac { \pi } { 2 } - 2 \right)$ and $\cot \left( \frac { \pi } { 2 } - \frac { 1 } { 3 } \right)$ ?

Evaluate each function.Round your answers to four decimal places. ? Csc3 and $\tan \frac { 1 } { 5 }$ ?

Evaluate each function.Round your answers to four decimal places.? $\cot \left( \frac { \pi } { 15 } \right)$ and $\tan \frac { \pi } { 15 }$ ?

Evaluate each function.Round your answers to four decimal places. Cos17°36' and sin67°23'

Evaluate each function.Round your answers to four decimal places. Sec0.74 and cos0.74

Evaluate each function.Round your answers to four decimal places. Sec48°38' and csc31°57'

Evaluate each function.Round your answers to four decimal places. Sin22.3° and csc22.3°

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°