Question 1

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°
​

Accepted Answer

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

Question 2

Construct an appropriate triangle to complete the table. $\left( 0 ^ { \circ } \leq \theta \leq 90 ^ { \circ } , 0 ^ { \circ } \leq \theta \leq \frac { \pi } { 2 } \right)$ $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \text { rad } ) & \text { Function Value } \
\hline \tan & & \frac { \pi } { 2 } & \
\hline
\end{array}$$
?

Accepted Answer

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) ? $$\begin{array} { | c | c | c | c | } 
\hline \text { Function } & \theta ( \mathrm { deg } ) & \theta ( \mathrm { rad } ) & \text { Function Value } \
\hline \tan & 30 ^ { \circ } & \frac { \pi } { 2 } & \frac { \sqrt { 3 } } { 3 } \
\hline
\end{array}$$

Question 3

Using the figure below,if ? = 20° and y = 16,determine the exact value of r.

Accepted Answer

A)  $$r = \frac { 5 } { \cos 4 ^ { \circ } }$$ 
B) ? $r = \frac { 16 } { \cos 20 ^ { \circ } }$ 
C) ? $r = \frac { 4 } { \csc 5 ^ { \circ } }$ 
D) ? $r = \frac { 16 } { \tan 20 ^ { \circ } }$ 
E) ? $r = \frac { 16 } { \sin 20 ^ { \circ } }$

Question 4

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

Accepted Answer

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

Question 5

Using the figure below,if ? = 33° and y = 9,determine the exact value of x.

Accepted Answer

A)  $x = \frac { 3 } { \sin 11 ^ { \circ } }$ 
B) ? $x = \frac { 9 } { \tan 33 ^ { \circ } }$ 
C) ? $x = \frac { 11 } { \tan 3 ^ { \circ } }$ 
D) ? $x = \frac { 9 } { \cot 33 ^ { \circ } }$ 
E) ? $x = \frac { 33 } { \csc 9 ^ { \circ } }$

Question 6

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

Accepted Answer

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 $\sin \left( 90 ^ { \circ } - \beta \right) = \frac { 4 \sqrt { 5 } } { 5 }$

Question 7

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. ?

Accepted Answer

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. )

Question 8

Find the exact value of csc ?,using the triangle shown in the figure below,if $a = 4$ and $b = 3$ .

Accepted Answer

A) ? $\frac { 3 } { 5 }$ 
B) ? $\frac { 4 } { 3 }$ 
C) ? $\frac { 5 } { 4 }$ 
D) ? $\frac { 4 } { 5 }$ 
E) ? $\frac { 5 } { 3 }$

Question 9

Given $\sec \theta = \sqrt { 10 }$ and tan ? = 3,determine the following. ?
Cos(90° - ?)
?

Accepted Answer

A) ?cos(90° - ?)= $\frac { 1 } { 3 }$ 
B) ?cos(90° - ?)= $\frac { 3 \sqrt { 10 } } { 10 }$ 
C) ?cos(90° - ?)= $\frac { \sqrt { 10 } } { 10 }$ 
D) ?cos(90° - ?)= 3 
E) undefined

Question 10

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

Accepted Answer

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 ? = $\frac { 3 } { 4 }$

Question 11

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

Accepted Answer

A)  $\cos \theta = 9$ 
B) ? $\cos \theta = \frac { 1 } { 9 }$ 
C) ? $\cos \theta = - \frac { 1 } { 9 }$ 
D) ? $\cos \theta = - 9$ 
E) ? $\cos \theta = 0$

Question 12

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. )  ?

Accepted Answer

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 ? = $\frac { 4 } { 5 }$
?

Question 13

Will Barrow wanted to know how tall the flagpole was in front of his school.To find its height,he drove a stake into the ground at the tip of the flagpole's shadow and recorded the angle of elevation at two different times during the day.He then measured the distance between the stakes.Will's data is below: Stake
Time
Angle of Elevation
A
2:00 PM
82°
B
3:00 PM
​61°
Distance between stakes A & B
10 feet  Determine the height of the flagpole.Round your answer to nearest foot.

Accepted Answer

A) 22 feet 
B) 24 feet 
C) 20 feet 
D) 26 feet 
E) 18 feet

Question 14

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° - ?)
?

Accepted Answer

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 $\csc \left( 90 ^ { \circ } - \theta \right) = - 5$

Question 15

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°

Accepted Answer

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

Question 16

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

Accepted Answer

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

Exam 25: Right Triangle Trigonometry

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°

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

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 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. ?

Given $\sec \theta = \sqrt { 10 }$ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

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

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° - ?) ?

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°

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

Exam 25: Right Triangle Trigonometry

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° ​

Using the figure below,if ? = 20° and y = 16,determine the exact value of r.

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​ ?

Using the figure below,if ? = 33° and y = 9,determine the exact value of x.

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 exact value of csc ?,using the triangle shown in the figure below,if a=4a = 4a=4 and b=3b = 3b=3 .

Given sec⁡θ=10\sec \theta = \sqrt { 10 }secθ=10​ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

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

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 ? ?

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. ) ?

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° - ?) ?

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°

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

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°

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

Given $\sec \theta = \sqrt { 10 }$ and tan ? = 3,determine the following. ? Cos(90° - ?) ?

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

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° - ?) ?

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°

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