Question 1

Use the fundamental identities to find the value of the trigonometric function.
-Find $\tan \theta$, given that $\cos \theta = - 0.55919290$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $1.482561$ 
B)  $2.048899$ 
C)  $- 1.4825610$ 
D)  $- 2.0488990$ 
A)  $1.482561$ 
B)  $2.048899$ 
C)  $- 1.4825610$ 
D)  $- 2.0488990$ C

Question 2

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\cot \theta = 1.5443661$

Accepted Answer

A)  $32.9236568 ^ { \circ }$ 
B)  $40.3544940 ^ { \circ }$ 
C)  $57.0763431 ^ { \circ }$ 
D)  $49.6455060 ^ { \circ }$ 
A)  $32.9236568 ^ { \circ }$ 
B)  $40.3544940 ^ { \circ }$ 
C)  $57.0763431 ^ { \circ }$ 
D)  $49.6455060 ^ { \circ }$ A

Question 3

Find the exact value of the expression.
-$\sec \theta = - \sqrt { 2 }$

Accepted Answer

A)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
A)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $225 ^ { \circ }$ B

Question 4

Find the exact value of the expression.
-$\sin 945 ^ { \circ }$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $- \frac { \sqrt { 3 } } { 2 }$ 
D)  $2 \sqrt { 3 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $- \frac { \sqrt { 3 } } { 2 }$ 
D)  $2 \sqrt { 3 }$

Question 5

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$87 ^ { \circ } 13 ^ { \prime } 49 ^ { \prime \prime }$

Accepted Answer

A)  $87.29 ^ { \circ }$ 
B)  $87.24 ^ { \circ }$ 
C)  $87.23 ^ { \circ }$ 
D)  $87.19 ^ { \circ }$ 
A)  $87.29 ^ { \circ }$ 
B)  $87.24 ^ { \circ }$ 
C)  $87.23 ^ { \circ }$ 
D)  $87.19 ^ { \circ }$

Question 6

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { B } = 58.45 ^ { \circ } , \mathrm { a } = 480.7 \mathrm {~m}$$
Give side lengths to two decimal places.

Accepted Answer

A)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 830.97 \mathrm {~m} ; \mathrm { c } = 905.12 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 782.90 \mathrm {~m} ; \mathrm { c } = 918.69 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 734.83 \mathrm {~m} ; \mathrm { c } = 918.69 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 782.90 \mathrm {~m} ; \mathrm { c } = 931.34 \mathrm {~m}$ 
A)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 830.97 \mathrm {~m} ; \mathrm { c } = 905.12 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 782.90 \mathrm {~m} ; \mathrm { c } = 918.69 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 734.83 \mathrm {~m} ; \mathrm { c } = 918.69 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 782.90 \mathrm {~m} ; \mathrm { c } = 931.34 \mathrm {~m}$

Question 7

Identify the quadrant for the angle $\theta$ satisfying the following conditions.
-$\cot \theta > 0 \text { and } \sin \theta < 0$

Accepted Answer

A)  Quadrant IV 
B)  Quadrant II 
C)  Quadrant III 
D)  Quadrant I 
A)  Quadrant IV 
B)  Quadrant II 
C)  Quadrant III 
D)  Quadrant I

Question 8

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-$295 ^ { \circ }$

Accepted Answer

A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$
  
C)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
D)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$
  
A)  $65 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $755 ^ { \circ }$ and $- 105 ^ { \circ }$
  
C)  $85 ^ { \circ }$ and $- 95 ^ { \circ }$
  
D)  $655 ^ { \circ }$ and $- 65 ^ { \circ }$

Question 9

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-The length of the base of an isosceles triangle is $28.35$ meters. Each base angle is $29.73 ^ { \circ }$. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Accepted Answer

A)  $16.32 \mathrm {~m}$ 
B)  $28.58 \mathrm {~m}$ 
C)  $24.82 \mathrm {~m}$ 
D)  $32.65 \mathrm {~m}$ 
A)  $16.32 \mathrm {~m}$ 
B)  $28.58 \mathrm {~m}$ 
C)  $24.82 \mathrm {~m}$ 
D)  $32.65 \mathrm {~m}$

Question 10

Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\sin \theta = - \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Accepted Answer

A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 4 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$ 
A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 4 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$

Question 11

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal
side of $\theta$ (3, 6) 
-$( 6,2 )$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { B } = 68 ^ { \circ } 35 ^ { \prime } , \mathrm { b } = 8 \mathrm {~km}$$
Round side lengths to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 8.6 \mathrm {~km} ; \mathrm { a } = 21.7 \mathrm {~km}$ 
B)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 21.9 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
C)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 8.6 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
D)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 21.9 \mathrm {~km} ; \mathrm { a } = 8.6 \mathrm {~km}$ 
A)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 8.6 \mathrm {~km} ; \mathrm { a } = 21.7 \mathrm {~km}$ 
B)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 21.9 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
C)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 8.6 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
D)  $\mathrm { A } = 21 ^ { \circ } 25 ^ { \prime } ; \mathrm { c } = 21.9 \mathrm {~km} ; \mathrm { a } = 8.6 \mathrm {~km}$

Question 13

Find the exact value of the expression.
-$\sec 1215 ^ { \circ }$

Accepted Answer

A)  2 
B)  $\frac { \sqrt { 2 } } { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 3 }$ 
A)  2 
B)  $\frac { \sqrt { 2 } } { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 3 }$

Question 14

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the
indicated trig function for $\theta$
-$( 0 , - 2 ) ;$ Find $\cos \theta$

Accepted Answer

A)  $- 2$ 
B)  0 
C)  1 
D)  2 
A)  $- 2$ 
B)  0 
C)  1 
D)  2

Question 15

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $17 ^ { \circ }$ and $34 ^ { \circ }$ 
B)  $15 ^ { \circ }$ and $30 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
D)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
A)  $17 ^ { \circ }$ and $34 ^ { \circ }$ 
B)  $15 ^ { \circ }$ and $30 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
D)  $30 ^ { \circ }$ and $60 ^ { \circ }$

Question 16

Find the reference angle for the given angle.
--2.7°

Accepted Answer

A)  87.8° 
B)  3.2° 
C)  87.3° 
D)  2.7° 
A)  87.8° 
B)  3.2° 
C)  87.3° 
D)  2.7°

Question 17

Without using a calculator, give the exact trigonometric function value with rational denominator.
-Find the exact value of x in the figure.

Accepted Answer

A)  $\frac { 8 \sqrt { 6 } } { 3 }$ 
B)  $31 \sqrt { 6 }$ 
C)  $\frac { 26 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 32 \sqrt { 6 } } { 3 }$ 
A)  $\frac { 8 \sqrt { 6 } } { 3 }$ 
B)  $31 \sqrt { 6 }$ 
C)  $\frac { 26 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 32 \sqrt { 6 } } { 3 }$

Question 18

An equation of the terminal side of an angle $\theta$ in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of $\theta$ . Do not use a calculator.
-$- 6 x - 5 y = 0 , x \leq 0 ; \quad$ Find $\sec \theta$

Accepted Answer

A)  $- \frac { \sqrt { 61 } } { 5 }$ 
B)  $- \frac { 5 \sqrt { 61 } } { 61 }$ 
C)  $- \frac { 6 } { 5 }$ 
D)  $- \frac { 5 } { 6 }$ 
A)  $- \frac { \sqrt { 61 } } { 5 }$ 
B)  $- \frac { 5 \sqrt { 61 } } { 61 }$ 
C)  $- \frac { 6 } { 5 }$ 
D)  $- \frac { 5 } { 6 }$

Question 19

Use the fundamental identities to find the value of the trigonometric function.
-Find $\sec \theta$, given that $\tan \theta = 0.44522869$ and $\theta$ is in quadrant $\mathrm { I }$.

Accepted Answer

A)  $1.2021766$ 
B)  $- 1.0946363$ 
C)  $1.0946363$ 
D)  $- 1.2021766$ 
A)  $1.2021766$ 
B)  $- 1.0946363$ 
C)  $1.0946363$ 
D)  $- 1.2021766$

Question 20

Evaluate the function requested. Write your answer as a fraction in lowest terms.
- 
Find $\sin \mathrm { A }$.

Accepted Answer

A)  $\sin \mathrm { A } = \frac { 4 } { 3 }$ 
B)  $\sin A = \frac { 5 } { 4 }$ 
C)  $\sin \mathrm { A } = \frac { 4 } { 5 }$ 
D)  $\sin A = \frac { 3 } { 5 }$ 
A)  $\sin \mathrm { A } = \frac { 4 } { 3 }$ 
B)  $\sin A = \frac { 5 } { 4 }$ 
C)  $\sin \mathrm { A } = \frac { 4 } { 5 }$ 
D)  $\sin A = \frac { 3 } { 5 }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\cos \theta = - 0.55919290$ and $\theta$ is in quadrant II.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\cot \theta = 1.5443661$

Find the exact value of the expression. - $\sec \theta = - \sqrt { 2 }$

Find the exact value of the expression. - $\sin 945 ^ { \circ }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $87 ^ { \circ } 13 ^ { \prime } 49 ^ { \prime \prime }$

Identify the quadrant for the angle $\theta$ satisfying the following conditions. - $\cot \theta > 0 \text { and } \sin \theta < 0$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $295 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\sin \theta = - \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Find the exact value of the expression. - $\sec 1215 ^ { \circ }$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ - $( 0 , - 2 ) ;$ Find $\cos \theta$

Find the measure of each angle in the problem. -

Find the reference angle for the given angle. --2.7°

Without using a calculator, give the exact trigonometric function value with rational denominator. -Find the exact value of x in the figure.

An equation of the terminal side of an angle $\theta$ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of $\theta$ . Do not use a calculator. - $- 6 x - 5 y = 0 , x \leq 0 ; \quad$ Find $\sec \theta$

Use the fundamental identities to find the value of the trigonometric function. -Find $\sec \theta$ , given that $\tan \theta = 0.44522869$ and $\theta$ is in quadrant $\mathrm { I }$ .

Evaluate the function requested. Write your answer as a fraction in lowest terms. - $Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find \sin \mathrm { A } .$ Find $\sin \mathrm { A }$ .

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 6: Trigonometric Functions

Use the fundamental identities to find the value of the trigonometric function. -Find tan⁡θ\tan \thetatanθ , given that cos⁡θ=−0.55919290\cos \theta = - 0.55919290cosθ=−0.55919290 and θ\thetaθ is in quadrant II.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - cot⁡θ=1.5443661\cot \theta = 1.5443661cotθ=1.5443661

Find the exact value of the expression. - sec⁡θ=−2\sec \theta = - \sqrt { 2 }secθ=−2​

Find the exact value of the expression. - sin⁡945∘\sin 945 ^ { \circ }sin945∘

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 87∘13′49′′87 ^ { \circ } 13 ^ { \prime } 49 ^ { \prime \prime }87∘13′49′′

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - B=58.45∘,a=480.7 m\mathrm { B } = 58.45 ^ { \circ } , \mathrm { a } = 480.7 \mathrm {~m}B=58.45∘,a=480.7 m Give side lengths to two decimal places.

Identify the quadrant for the angle θ\thetaθ satisfying the following conditions. - cot⁡θ>0 and sin⁡θ<0\cot \theta > 0 \text { and } \sin \theta < 0cotθ>0 and sinθ<0

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - 295∘295 ^ { \circ }295∘

Use the fundamental identities to find the value of the trigonometric function. -Find csc⁡θ\csc \thetacscθ , given that sin⁡θ=−23\sin \theta = - \frac { 2 } { 3 }sinθ=−32​ and θ\thetaθ is in quadrant IV.

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point is on the terminal side of θ\thetaθ (3, 6) - (6,2)( 6,2 )(6,2)

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - B=68∘35′,b=8 km\mathrm { B } = 68 ^ { \circ } 35 ^ { \prime } , \mathrm { b } = 8 \mathrm {~km}B=68∘35′,b=8 km Round side lengths to one decimal place.

Find the exact value of the expression. - sec⁡1215∘\sec 1215 ^ { \circ }sec1215∘

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ - (0,−2);( 0 , - 2 ) ;(0,−2); Find cos⁡θ\cos \thetacosθ