Question 1

Find an equation for the graph.
-

Accepted Answer

A)  $y = - 3 \sin ( 3 x )$ 
B)  $y = - 3 \cos ( 3 x )$ 
C)  $y = - 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
A)  $y = - 3 \sin ( 3 x )$ 
B)  $y = - 3 \cos ( 3 x )$ 
C)  $y = - 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = 3 \cos \left( \frac { 1 } { 3 } x \right)$

Question 2

Answer the question.
-Which one of the equations below matches the graph?

Accepted Answer

A)  $y = - 3 \sin ( 4 x )$ 
B)  $y = 3 \cos \left( \frac { 1 } { 4 } x \right)$ 
C)  $y = 3 \cos ( 4 x )$ 
D)  $y = 3 \sin \left( \frac { 1 } { 4 } x \right)$ 
A)  $y = - 3 \sin ( 4 x )$ 
B)  $y = 3 \cos \left( \frac { 1 } { 4 } x \right)$ 
C)  $y = 3 \cos ( 4 x )$ 
D)  $y = 3 \sin \left( \frac { 1 } { 4 } x \right)$

Question 3

Solve the problem.
-Which of the following trigonometric values are negative? I. $\sin \left( - 292 ^ { \circ } \right)$
II. $\tan \left( - 193 ^ { \circ } \right)$
III. $\cos \left( - 207 ^ { \circ } \right)$
IV. $\cot 222 ^ { \circ }$

Accepted Answer

A)  II, III, and IV 
B)  I and III 
C)  III only 
D)  II and III 
A)  II, III, and IV 
B)  I and III 
C)  III only 
D)  II and III

Question 4

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$$\csc \left( - \frac { \pi } { 3 } \right)$$

Accepted Answer

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

Question 5

Name the quadrant in which the angle θ lies.
-$\sin \theta > 0 , \quad \cos \theta < 0$

Accepted Answer

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

Question 6

Without graphing the function, determine its amplitude or period as requested.
-$y = - 4 \sin 5 x \quad$ Find the amplitude.

Accepted Answer

A)  $\frac { \pi } { 4 }$ 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  4 
A)  $\frac { \pi } { 4 }$ 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  4

Question 7

Find the length s. Round the answer to three decimal places.
-

Accepted Answer

A)  $4.084 \mathrm {~cm}$ 
B)  $3.63 \mathrm {~cm}$ 
C)  $4.992 \mathrm {~cm}$ 
D)  $4.538 \mathrm {~cm}$ 
A)  $4.084 \mathrm {~cm}$ 
B)  $3.63 \mathrm {~cm}$ 
C)  $4.992 \mathrm {~cm}$ 
D)  $4.538 \mathrm {~cm}$

Question 8

Find the area A. Round the answer to three decimal places.
-

Accepted Answer

A)  $0.778 \mathrm{~cm}^{2}$ 
B) $1.222 \mathrm{~cm}^{2}$ 
C) $4.887 \mathrm{~cm}^{2}$ 
D) $2.443\mathrm{~cm}^{2}$ 
A)  $0.778 \mathrm{~cm}^{2}$ 
B) $1.222 \mathrm{~cm}^{2}$ 
C) $4.887 \mathrm{~cm}^{2}$ 
D) $2.443\mathrm{~cm}^{2}$

Question 9

Solve the problem.
-$\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 } \quad$ Find $\tan \theta$.

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 2 \sqrt { 5 } } { 5 }$ 
C)  $\frac { 3 \sqrt { 5 } } { 5 }$ 
D)  $\frac { \sqrt { 5 } } { 2 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 2 \sqrt { 5 } } { 5 }$ 
C)  $\frac { 3 \sqrt { 5 } } { 5 }$ 
D)  $\frac { \sqrt { 5 } } { 2 }$

Question 10

Find the exact value of the indicated trigonometric function of $\theta$
-$\sin \theta = - \frac { 4 } { 9 } , \tan \theta > 0 \quad$ Find $\sec \theta$.

Accepted Answer

A)  $- \frac { 9 \sqrt { 65 } } { 65 }$ 
B)  $- \frac { \sqrt { 65 } } { 9 }$ 
C)  $- \frac { 4 \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 9 } } { 4 }$ 
A)  $- \frac { 9 \sqrt { 65 } } { 65 }$ 
B)  $- \frac { \sqrt { 65 } } { 9 }$ 
C)  $- \frac { 4 \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 9 } } { 4 }$

Question 11

Find the exact value of the indicated trigonometric function of $\theta$
-$\sec \theta = \frac { 9 } { 2 } , \quad \theta$ in quadrant IV $\quad$ Find $\tan \theta$.

Accepted Answer

A)  $- \frac { \sqrt { 77 } } { 9 }$ 
B)  $- \frac { \sqrt { 77 } } { 2 }$ 
C)  $- \sqrt { 77 }$ 
D)  $- \frac { 9 } { 2 }$ 
A)  $- \frac { \sqrt { 77 } } { 9 }$ 
B)  $- \frac { \sqrt { 77 } } { 2 }$ 
C)  $- \sqrt { 77 }$ 
D)  $- \frac { 9 } { 2 }$

Question 12

Graph the sinusoidal function.
-$y=2 \sin (4 x)$
 
 A)

Accepted Answer

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

Question 13

Graph the function.
-$y=\csc \left(x-\frac{\pi}{3}\right)$
  A)

Accepted Answer

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

Question 14

Solve the problem.
-In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of $$2.4 \times 10 ^ { 4 }$$ miles. The orbit is circular, and one revolution around Earth takes 10.1 days. Assuming the radius of the Earth is 3960
Miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile.

Accepted Answer

A)  115 mph 
B)  725 mph 
C)  15,322 mph 
D)  622 mph 
A)  115 mph 
B)  725 mph 
C)  15,322 mph 
D)  622 mph

Question 15

Solve the problem.
-A rotating beacon is located 4 ft from a wall. If the distance from the beacon to the point on the wall where the beacon is aimed is given by $$a = 4 | \sec 2 \pi t |$$ where t is in seconds, find a when t = 0.34 seconds. Round your answer to the nearest hundredth.

Accepted Answer

A)  7.88 ft 
B)  8.30 ft 
C)  7.47 ft 
D)  -7.47 ft 
A)  7.88 ft 
B)  8.30 ft 
C)  7.47 ft 
D)  -7.47 ft

Question 16

Use transformations to graph the function.
-$y=-2 \sin x$
 
 A)

Accepted Answer

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

Question 17

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\tan 42 ^ { \circ }$

Accepted Answer

A)  $2.42$ 
B)  $0.90$ 
C)  $2.29$ 
D)  $1.03$ 
A)  $2.42$ 
B)  $0.90$ 
C)  $2.29$ 
D)  $1.03$

Question 18

Graph the function. Show at least one period.
-$y=4 \sin (3 \pi x+3)$
 
 A)

Accepted Answer

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

Question 19

Solve the problem.
-A wheel of radius 3.4 feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Accepted Answer

A)  0.19 radians/sec 
B)  5.7 radians/sec 
C)  5.3 radians/sec 
D)  0.92 radians/sec 
A)  0.19 radians/sec 
B)  5.7 radians/sec 
C)  5.3 radians/sec 
D)  0.92 radians/sec

Question 20

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator.
-$\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

Accepted Answer

A)  -1 
B)  40 
C)  1 
D)  0 
A)  -1 
B)  40 
C)  1 
D)  0

Find an equation for the graph. -

Answer the question. -Which one of the equations below matches the graph?

Solve the problem. -Which of the following trigonometric values are negative? I. $\sin \left( - 292 ^ { \circ } \right)$ II. $\tan \left( - 193 ^ { \circ } \right)$ III. $\cos \left( - 207 ^ { \circ } \right)$ IV. $\cot 222 ^ { \circ }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - \frac { \pi } { 3 } \right)$

Name the quadrant in which the angle θ lies. - $\sin \theta > 0 , \quad \cos \theta < 0$

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \sin 5 x \quad$ Find the amplitude.

Find the length s. Round the answer to three decimal places. -

Find the area A. Round the answer to three decimal places. -

Solve the problem. - $\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 } \quad$ Find $\tan \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sin \theta = - \frac { 4 } { 9 } , \tan \theta > 0 \quad$ Find $\sec \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sec \theta = \frac { 9 } { 2 } , \quad \theta$ in quadrant IV $\quad$ Find $\tan \theta$ .

Solve the problem. -A rotating beacon is located 4 ft from a wall. If the distance from the beacon to the point on the wall where the beacon is aimed is given by $a = 4 | \sec 2 \pi t |$ where t is in seconds, find a when t = 0.34 seconds. Round your answer to the nearest hundredth.

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 42 ^ { \circ }$

Solve the problem. -A wheel of radius 3.4 feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 5: Trigonometric Functions

Find an equation for the graph. -

Answer the question. -Which one of the equations below matches the graph?

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - csc⁡(−π3)\csc \left( - \frac { \pi } { 3 } \right)csc(−3π​)

Name the quadrant in which the angle θ lies. - sin⁡θ>0,cos⁡θ<0\sin \theta > 0 , \quad \cos \theta < 0sinθ>0,cosθ<0

Without graphing the function, determine its amplitude or period as requested. - y=−4sin⁡5xy = - 4 \sin 5 x \quady=−4sin5x Find the amplitude.

Find the length s. Round the answer to three decimal places. -

Find the area A. Round the answer to three decimal places. -

Solve the problem. - sin⁡θ=74,cos⁡θ=34\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 } \quadsinθ=47​​,cosθ=43​ Find tan⁡θ\tan \thetatanθ .

Find the exact value of the indicated trigonometric function of θ\thetaθ - sin⁡θ=−49,tan⁡θ>0\sin \theta = - \frac { 4 } { 9 } , \tan \theta > 0 \quadsinθ=−94​,tanθ>0 Find sec⁡θ\sec \thetasecθ .

Find the exact value of the indicated trigonometric function of θ\thetaθ - sec⁡θ=92,θ\sec \theta = \frac { 9 } { 2 } , \quad \thetasecθ=29​,θ in quadrant IV \quad Find tan⁡θ\tan \thetatanθ .

Graph the sinusoidal function. - y=2sin⁡(4x)y=2 \sin (4 x)y=2sin(4x) A) B) C) D)

Graph the function. - y=csc⁡(x−π3)y=\csc \left(x-\frac{\pi}{3}\right)y=csc(x−3π​) A) B) C) D)

Use transformations to graph the function. - y=−2sin⁡xy=-2 \sin xy=−2sinx A) B) C) D)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - tan⁡42∘\tan 42 ^ { \circ }tan42∘

Graph the function. Show at least one period. - y=4sin⁡(3πx+3)y=4 \sin (3 \pi x+3)y=4sin(3πx+3) A) B) C) D)

Solve the problem. -A wheel of radius 3.4 feet is moving forward at 18 feet per second. How fast is the wheel rotating?

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - tan⁡40∘cot⁡40∘\tan 40 ^ { \circ } \cot 40 ^ { \circ }tan40∘cot40∘

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - \frac { \pi } { 3 } \right)$

Name the quadrant in which the angle θ lies. - $\sin \theta > 0 , \quad \cos \theta < 0$

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \sin 5 x \quad$ Find the amplitude.

Solve the problem. - $\sin \theta = \frac { \sqrt { 7 } } { 4 } , \cos \theta = \frac { 3 } { 4 } \quad$ Find $\tan \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sin \theta = - \frac { 4 } { 9 } , \tan \theta > 0 \quad$ Find $\sec \theta$ .

Find the exact value of the indicated trigonometric function of $\theta$ - $\sec \theta = \frac { 9 } { 2 } , \quad \theta$ in quadrant IV $\quad$ Find $\tan \theta$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 42 ^ { \circ }$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\tan 40 ^ { \circ } \cot 40 ^ { \circ }$