Question 1

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?sin 30° = $\frac { 1 } { 2 }$ ,cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ?
?sin 60° and cos 60°
A)?sin 60° = 2 and cos 60° = $\frac { 1 } { 2 }$
B)?sin 60° = $\sqrt { 3 }$ and cos 60° = $\frac { 1 } { 2 }$
C)?sin 60° = $\frac { \sqrt { 3 } } { 2 }$ and cos 60° = $\sqrt { 2 }$
D)?sin 60° = $\frac { \sqrt { 3 } } { 2 }$ and cos 60° = $\frac { 1 } { 2 }$
E)?sin 60° = $\frac { \sqrt { 3 } } { 2 }$ and cos 60° = 2

Accepted Answer

The values of sin 60° and cos 60° are derived from the cofunction identity and the given values. Since sin 30° = 1/2, and cos 30° = sqrt(3)/2, by the complementary angles in trigonometry (sin(90° - θ) = cos θ), sin 60° = cos 30° = sqrt(3)/2, and cos 60° = sin 30° = 1/2.

Question 2

Use a graphing utility to complete the table. $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & & & & & \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.5 & 0.77 & 0.87 & 0.5 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0.94 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0.5 & 0.64 & 0.77 & 0.87 & 0.94 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 20 ^ { \circ } & 30 ^ { \circ } & 40 ^ { \circ } & 50 ^ { \circ } & 60 ^ { \circ } \
\hline \cos \theta & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline \sin \left( 90 ^ { \circ } - \theta \right) & 0 & 0.87 & 0.77 & 0.64 & 0.5 \
\hline
\end{array}$$

Accepted Answer

The cosine of an angle is equal to the sine of its complementary angle, i.e., $\cos(\theta) = \sin(90^\circ - \theta)$. The values in option C correctly reflect this identity for the given angles.

Question 3

Use a compass to sketch a quarter of a circle of radius 10 centimeters.Using a protractor, construct an angle of $a = 10 ^ { \circ }$ in standard position (see figure).Drop a perpendicular line from the point of intersection of the terminal side of the angle and the arc of the circle.By actual measurement,calculate the coordinates $( x , y )$ of the point of intersection and use these measurements to approximate the six trigonometric functions of a $\text { "a" }$ angle.(Round your answer to two decimal places. )?  ?
A)sin10° ? 0.98,cos10° ? 0.17,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 1.02,cot10° ? 5.67
B)sin10° ? 5.67,cos10° ? 1.02,tan10° ? 5.76, csc10° ? 0.18,sec10° ? 0.98,cot10° ? 5.67
?
C)sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 1.02,cot10° ? 5.67
?
D)sin10° ? 0.18,cos10° ? 0.98,tan10° ? 0.17, csc10° ? 10,sec10° ? 0.98,cot10° ? 5.76
?
E)sin10° ? 0.17,cos10° ? 0.98,tan10° ? 0.18, csc10° ? 5.76,sec10° ? 5.67,cot10° ? 1.02

Accepted Answer

From the diagram, we can see that the x-coordinate of the point of intersection is approximately 1 and the y-coordinate is approximately 0.17. 
Therefore, the six trigonometric functions are:

sin(10°) ≈ 0.17
cos(10°) ≈ 0.98
tan(10°) ≈ 0.18
csc(10°) ≈ 5.76
sec(10°) ≈ 1.02
cot(10°) ≈ 5.67

These values match those given in choice C.

Question 4

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\cos \beta = \frac { \sqrt { 5 } } { 4 }$ ? $\sec \beta \text { and } \sin \left( 90 ^ { \circ } - \beta \right)$ ?
A) $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
B)? $\sec \beta = \sqrt { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = 4$
C)? $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { \sqrt { 5 } } { 4 }$
D)? $\sec \beta = \frac { \sqrt { 5 } } { 4 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$
E)? $\sec \beta = \frac { 4 \sqrt { 5 } } { 5 }$ and $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$

Accepted Answer

Using the given function value of sine, we can determine the cosine using the cofunction identity:
cos(θ) = sin(90° - θ)
cos(30°) = sin(90° - 30°) = sin(60°) = √3/2

Using the given function value of tangent, we can determine the adjacent and hypotenuse using the Pythagorean identity:
tan(θ) = sin(θ) / cos(θ)
tan(45°) = sin(45°) / cos(45°) 
1 = sin(45°) / cos(45°)
cos(45°) = sin(45°) = 1/√2
Using the adjacent and hypotenuse, we can determine the sine using the Sokotoa identity:
sin(θ) = opposite / hypotenuse
sin(45°) = 1/√2 / √2 = 1/2

Question 5

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. ?sin ? = 1 and csc ? = 1
?
?
A)90° = $\frac { \pi } { 2 }$
B)?30° = $\frac { \pi } { 6 }$
C)?0° = 0
D)?60° = $\frac { \pi } { 3 }$
E)?45° = $\frac { \pi } { 4 }$

Accepted Answer

The sine function equals 1 only at $\theta = 90^\circ$ or $\theta = \frac{\pi}{2}$ radians. The cosecant (csc) function is the reciprocal of the sine function, and csc $\theta = 1$ also corresponds to sin $\theta = 1$, which occurs at the same angle.

Question 6

A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly.From point A the biologist walks downstream $x = 140$ feet and sights to point C (see figure).From this sighting,it is determined that ? = 54°.How wide is the river??  (Round your answer to three decimal places. ) ?
A)212.693
B)197.693
C)207.693
D)202.693
E)192.693

Accepted Answer

The answer of A biologist wants to know the width...

Question 7

You are skiing down a mountain with a vertical height of 1250 feet.The distance from the top of the mountain to the base is 2500 feet.What is the angle of elevation from the base to the top of the mountain? ?
A)60° = $\frac { \pi } { 3 }$
B)30° = $\frac { \pi } { 6 }$
C)0° = 0
D)90° = $\frac { \pi } { 2 }$
E)45° = $\frac { \pi } { 4 }$

Accepted Answer

The tangent of the angle of elevation can be found by taking the ratio of the vertical height to the horizontal distance:

tan θ = vertical height/horizontal distance
tan θ = 1250/2500
tan θ = 0.5

Using a calculator, we can find the inverse tangent (or arctan) of 0.5 to be approximately 30 degrees, so the answer is B) 30°.

Question 8

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive $x = 23$ miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place. )?  ?
A)10.3 mi
B)2.3 mi
C)4.3 mi
D)8.3 mi
E)6.3 mi

Accepted Answer

The answer of In traveling across flat land,you notice a...

Question 9

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. cos ? = 0 and tan ? = Not defined
?
?
A)90° = $\frac { \pi } { 2 }$
B)?60° = $\frac { \pi } { 3 }$
C)?0° = 0
D)?30° = $\frac { \pi } { 6 }$
E)?45° = $\frac { \pi } { 4 }$

Accepted Answer

The cosine of an angle is 0 at $90^\circ$ or $\frac{\pi}{2}$ radians, and the tangent is not defined at the same angles because it involves division by zero in the sine over cosine ratio.

Question 10

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ​
​sin 90° = 1,tan 90° = Not defined
Sin 0° and tan 0°
​
A)​sin 0° = 0 and tan 0° = 0
B)sin 0° = 1 and tan 0° = 1
C)​sin 0° = Not defined and tan 0° = Not defined
D)​sin 0° = Not defined and tan 0° = 1
E)​sin 0° = 1 and tan 0° = Not defined

Accepted Answer

Using the cofunction identity, we know that sin 0° = cos 90° = 0. 
Also, tan 0° = sin 0°/cos 0° = 0/1 = 0. Therefore, the correct choice is A).

Question 11

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ?
A) $$\sin 85 ^ { \circ } = \frac { h } { 20 }$$ (where h is height. )
B) $\cos 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height. )
C) $\cos 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height. )
D) $\sin 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height. )
E) $\tan 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height. )

Accepted Answer

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Here, the height $h$ is opposite the 85° angle, and the 20-meter line is the hypotenuse, so $\sin 85 ^ { \circ } = \frac { h } { 20 }$ is the correct equation.

Question 12

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. sec ? = $\sqrt { 2 }$ and cot ? = 1
?
?
A)45° = $\frac { \pi } { 4 }$
B)?90° = $\frac { \pi } { 2 }$
C)?0° = 0
D)?60° = $\frac { \pi } { 3 }$
E)?30° = $\frac { \pi } { 6 }$

Accepted Answer

sec θ = $\sqrt{2}$ corresponds to an angle of 45° or $\frac{\pi}{4}$ radians, and cot θ = 1 also corresponds to an angle of 45° or $\frac{\pi}{4}$ radians, since both sec and cot are equal to $\sqrt{2}$ and 1, respectively, at this angle in the first quadrant.

Question 13

Complete the table. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & & & & & \
\hline
\end{array}$$
(Round your answer to four decimal places. )

A)$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7833 & 0.8415 & 0.8912 & 0.932 \
\hline
\end{array}$$
B)$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0 & 1 & 2 & 3 & 4 \
\hline
\end{array}$$
C)$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.932 & 0.8912 & 0.8415 & 0.7833 & 0.7174 \
\hline
\end{array}$$
D)$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.7174 & 0.7174 & 0.8415 & 0.7174 & 0.932 \
\hline
\end{array}$$
E)$$\begin{array} { | c | c | c | c | c | c | } 
\hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline \sin \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \
\hline
\end{array}$$

Accepted Answer

The correct values for $\sin \theta$ are calculated using a scientific calculator or a mathematical software, and the values in option A are accurate to four decimal places.

Question 14

A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures $\theta$ .(Round your answers to one decimal places. ) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 5.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle } , \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 7.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 4.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 3.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 6.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$

Accepted Answer

To find the height of the balloon, we use the sine function in trigonometry because the height forms the opposite side of the right triangle, the tether line is the hypotenuse, and the angle $\theta$ is given. The formula is $\text{height} = \text{hypotenuse} \times \sin(\theta)$. For a 10-meter line:- At $50^\circ$, $\text{height} = 10 \times \sin(50^\circ) \approx 7.7$ meters.- At $40^\circ$, $\text{height} = 10 \times \sin(40^\circ) \approx 6.4$ meters.- At $30^\circ$, $\text{height} = 10 \times \sin(30^\circ) = 5$ meters (since $\sin(30^\circ) = 0.5$).- At $20^\circ$, $\text{height} = 10 \times \sin(20^\circ) \approx 3.4$ meters.- At $10^\circ$, $\text{height} = 10 \times \sin(10^\circ) \approx 1.7$ meters.

Question 15

A tapered shaft has a diameter of $x = 9$ centimeters at the small end and is 15 centimeters long (see figure).The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. )?  ? ?
A)10.57 cm
B)14.57 cm
C)12.57 cm
D)18.57 cm
E)16.57 cm

Accepted Answer

The answer of A tapered shaft has a diameter of...

Question 16

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\cos \theta = \frac { 1 } { 5 }$ ? sec ? and csc(90° - ?)
?
A)? $\sec \theta = \frac { 1 } { 5 }$ and $\csc \left( 90 ^ { \circ } - \theta \right) = \frac { 1 } { 5 }$
B) $\sec \theta = 5$ and $\csc \left( 90 ^ { \circ } - \theta \right) = 5$
C)? $\sec \theta = \frac { 1 } { 5 }$ and $\csc \left( 90 ^ { \circ } - \theta \right) = 5$
D)? $\sec \theta = 5$ and $\csc \left( 90 ^ { \circ } - \theta \right) = \frac { 1 } { 5 }$
E)? $\sec \theta = - 5$ and $\csc \left( 90 ^ { \circ } - \theta \right) = - 5$

Accepted Answer

$\sec \theta = \frac{1}{\cos \theta} = 5$ and $\csc(90° - \theta) = \frac{1}{\sin(90° - \theta)}$. Since $\sin(90° - \theta) = \cos \theta$, $\csc(90° - \theta) = \frac{1}{\cos \theta} = 5$.

Question 17

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower $x = 100$ feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire. ??  ?
A)166.6 ft
B)?146.6 ft
C)?156.6 ft
D)?161.6 ft
E)?151.6 ft

Accepted Answer

The answer of A guy wire runs from the ground...

Question 18

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions.? $\sec \theta = 9$ ? cos ?
?
A) $\cos \theta = 9$
B)? $\cos \theta = \frac { 1 } { 9 }$
C)? $\cos \theta = - \frac { 1 } { 9 }$
D)? $\cos \theta = - 9$
E)? $\cos \theta = 0$

Accepted Answer

The secant function is the reciprocal of the cosine function, so if $\sec \theta = 9$, then $\cos \theta = \frac{1}{9}$.

Question 19

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. ) ​
A)45 m
B)41 m
C)43 m
D)49 m
E)47 m

Accepted Answer

To find the height of the balloon, we can use the trigonometric function sine, since we have the angle and the hypotenuse (the length of the tether). The sine of an angle in a right triangle is the opposite side (height of the balloon in this case) over the hypotenuse (the length of the tether). So, sin(55°) = height / 50 meters. Rearranging to solve for height gives us height = 50 * sin(55°). Using a calculator, we find that height ≈ 40.96 meters, which rounds to 41 meters.

Question 20

Use the given function value(s),and trigonometric identities (including the cofunction identities),to find the indicated trigonometric functions. ?? $\cot \alpha = 3$ ? $\tan \alpha \text { and } \cot \left( 90 ^ { \circ } - \alpha \right)$ ?
A)? $\tan \alpha = - \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = - \frac { 1 } { 3 }$
B)? $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$
C) $\tan \alpha = \frac { 1 } { 3 }$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$
D)? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = 3$
E)? $\tan \alpha = 3$ and $\cot \left( 90 ^ { \circ } - \alpha \right) = \frac { 1 } { 3 }$

Accepted Answer

The answer of Use the given function value(s),and trigonometric identities...

Quiz 25: Right Triangle Trigonometry

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions. ?sin 30° = $\frac { 1 } { 2 }$ ,cos 30° = $\frac { \sqrt { 3 } } { 2 }$ ? ?sin 60° and cos 60°

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions.? $\cos \beta = \frac { \sqrt { 5 } } { 4 }$ ? $\sec \beta \text { and } \sin \left( 90 ^ { \circ } - \beta \right)$ ?

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. ?sin ? = 1 and csc ? = 1 ? ?

You are skiing down a mountain with a vertical height of 1250 feet.The distance from the top of the mountain to the base is 2500 feet.What is the angle of elevation from the base to the top of the mountain? ?

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak) is 3.5°.After you drive $x = 23$ miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.(Round your answer upto one decimal place. ) ? ?

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. cos ? = 0 and tan ? = Not defined ? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions. sin 90° = 1,tan 90° = Not defined Sin 0° and tan 0°

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ?

Find the values of ? in degrees $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right)$ and radians $\left( 0 < \theta < \frac { \pi } { 2 } \right)$ without the aid of a calculator. sec ? = $\sqrt { 2 }$ and cot ? = 1 ? ?

Complete the table. $\begin{array} { | c | c | c | c | c | c | } \hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \\\hline \sin \theta & & & & & \\\hline\end{array}$ (Round your answer to four decimal places. )

A tapered shaft has a diameter of $x = 9$ centimeters at the small end and is 15 centimeters long (see figure) .The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. ) ? ? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions.? $\cos \theta = \frac { 1 } { 5 }$ ? sec ? and csc(90° - ?) ?

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower $x = 100$ feet above the ground.The angle formed between the wire and the ground is 43° (see figure) .How long is the guy wire. ?? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions.? $\sec \theta = 9$ ? cos ? ?

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. )

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions. ?? $\cot \alpha = 3$ ? $\tan \alpha \text { and } \cot \left( 90 ^ { \circ } - \alpha \right)$ ?

Quiz 25: Right Triangle Trigonometry

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions. ?sin 30° = 12\frac { 1 } { 2 }21​ ,cos 30° = 32\frac { \sqrt { 3 } } { 2 }23​​ ? ?sin 60° and cos 60°

Find the values of ? in degrees (0∘≤θ≤90∘) \left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right) (0∘≤θ≤90∘) and radians (0<θ<π2) \left( 0 < \theta < \frac { \pi } { 2 } \right) (0<θ<2π​) without the aid of a calculator. ?sin ? = 1 and csc ? = 1 ? ?

You are skiing down a mountain with a vertical height of 1250 feet.The distance from the top of the mountain to the base is 2500 feet.What is the angle of elevation from the base to the top of the mountain? ?

Find the values of ? in degrees (0∘≤θ≤90∘) \left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right) (0∘≤θ≤90∘) and radians (0<θ<π2) \left( 0 < \theta < \frac { \pi } { 2 } \right) (0<θ<2π​) without the aid of a calculator. cos ? = 0 and tan ? = Not defined ? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions. ​ ​sin 90° = 1,tan 90° = Not defined Sin 0° and tan 0° ​

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ?

Find the values of ? in degrees (0∘≤θ≤90∘) \left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } \right) (0∘≤θ≤90∘) and radians (0<θ<π2) \left( 0 < \theta < \frac { \pi } { 2 } \right) (0<θ<2π​) without the aid of a calculator. sec ? = 2\sqrt { 2 }2​ and cot ? = 1 ? ?

Complete the table. θ0.80.911.11.2sin⁡θ\begin{array} { | c | c | c | c | c | c | } \hline \theta & 0.8 & 0.9 & 1 & 1.1 & 1.2 \\\hline \sin \theta & & & & & \\\hline\end{array}θsinθ​0.8​0.9​1​1.1​1.2​​ (Round your answer to four decimal places. )

A tapered shaft has a diameter of x=9x = 9x=9 centimeters at the small end and is 15 centimeters long (see figure) .The taper is 3°.Find the diameter d of the large end of the shaft.(Round your answer to two decimal places. ) ? ? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions.? cos⁡θ=15\cos \theta = \frac { 1 } { 5 }cosθ=51​ ? sec ? and csc(90° - ?) ?

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower x=100x = 100x=100 feet above the ground.The angle formed between the wire and the ground is 43° (see figure) .How long is the guy wire. ?? ?

Use the given function value(s) ,and trigonometric identities (including the cofunction identities) ,to find the indicated trigonometric functions.? sec⁡θ=9\sec \theta = 9secθ=9 ? cos ? ?

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. ) ​