Question 1

Solve the problem.
-What is the $y$-intercept of $y = \cos x$ ?

Accepted Answer

A)  0 
B)  $\pi$ 
C)  1 
D)  $\frac { \pi } { 2 }$ 
A)  0 
B)  $\pi$ 
C)  1 
D)  $\frac { \pi } { 2 }$

Question 2

Without graphing the function, determine its amplitude or period as requested.
-$y = - 4 \cos \frac { 1 } { 3 } x \quad$ Find the amplitude.

Accepted Answer

A)  $\frac { 4 \pi } { 3 }$ 
B)  4 
C)  $\frac { \pi } { 4 }$ 
D)  $6 \pi$ 
A)  $\frac { 4 \pi } { 3 }$ 
B)  4 
C)  $\frac { \pi } { 4 }$ 
D)  $6 \pi$

Question 3

Solve the problem.
-For what numbers $x , 0 \leq x \leq 2 \pi$, does $\cos x = 0$ ?

Accepted Answer

A)  0,1 
B)  $0 , \pi , 2 \pi$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  $0,1,2$ 
A)  0,1 
B)  $0 , \pi , 2 \pi$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  $0,1,2$

Question 4

Solve the problem.
-What is the domain of the sine function? A) all real numbers, except integral multiples of $\pi \left( 180 ^ { \circ } \right)$

Accepted Answer

B)  all real numbers 
C)  all real numbers from $- 1$ to 1 , inclusive 
D)  all real numbers, except odd multiples of $\frac { \pi } { 2 } \left( 90 ^ { \circ } \right)$ 
B)  all real numbers 
C)  all real numbers from $- 1$ to 1 , inclusive 
D)  all real numbers, except odd multiples of $\frac { \pi } { 2 } \left( 90 ^ { \circ } \right)$

Question 5

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

Accepted Answer

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

Question 6

Find the exact value of the expression. Do not use a calculator.
-$\cos 120 ^ { \circ } \tan 60 ^ { \circ }$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 2 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $- \frac { 1 } { 4 }$ 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 2 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $- \frac { 1 } { 4 }$

Question 7

Find the exact value of the indicated trigonometric function of $\theta$
-$\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quad$ Find $\cos \theta$

Accepted Answer

A)  $- \frac { 15 } { 17 }$ 
B)  $\frac { - 21 \sqrt { 41 } } { 41 }$ 
C)  $- 15$ 
D)  $\frac { 20 \sqrt { 41 } } { 41 }$ 
A)  $- \frac { 15 } { 17 }$ 
B)  $\frac { - 21 \sqrt { 41 } } { 41 }$ 
C)  $- 15$ 
D)  $\frac { 20 \sqrt { 41 } } { 41 }$

Question 8

Find the exact value. Do not use a calculator.
-$\sin \pi$

Accepted Answer

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

Question 9

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\sin 495 ^ { \circ }$

Accepted Answer

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

Question 10

Solve the problem.
-The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The rest force $F$, in Newtons, acting on a string pendulum is given by the formula
$$\mathrm { F } = \mathrm { mg } \sin \theta$$
where $\mathrm { m }$ is the mass in kilograms of the pendulum's bob, $g \approx 9.8$ meters per second per second is the acceleration due to gravity, and $\theta$ is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when $\mathrm { m } = 0.7$ kilogram and $\theta = 45 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a Newton.

Accepted Answer

A)  $4.7 \mathrm {~N}$ 
B)  $4.6 \mathrm {~N}$ 
C)  $5.8 \mathrm {~N}$ 
D)  $4.9 \mathrm {~N}$ 
A)  $4.7 \mathrm {~N}$ 
B)  $4.6 \mathrm {~N}$ 
C)  $5.8 \mathrm {~N}$ 
D)  $4.9 \mathrm {~N}$

Question 11

Find the exact value. Do not use a calculator.
-$\sin ( 4 \pi )$

Accepted Answer

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

Question 12

Find the exact value. Do not use a calculator.
-$$\sin 0$$

Accepted Answer

A)  1 
B)  0 
C)  $$\frac { \sqrt { 2 } } { 2 }$$ 
D)  undefined 
A)  1 
B)  0 
C)  $$\frac { \sqrt { 2 } } { 2 }$$ 
D)  undefined

Question 13

Find the phase shift of the function.
-$$y = 5 \sin \left( x - \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  5 units down 
B)  $\frac { \pi } { 4 }$ units to the right 
C)  5 units up 
D)  $\frac { \pi } { 4 }$ units to the left 
A)  5 units down 
B)  $\frac { \pi } { 4 }$ units to the right 
C)  5 units up 
D)  $\frac { \pi } { 4 }$ units to the left

Question 14

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 5,12 )$ Find $\sin \theta$

Accepted Answer

A)  $- \frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $\frac { 5 } { 13 }$ 
A)  $- \frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $\frac { 5 } { 13 }$

Question 15

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of
the indicated trigonometric function of t.
-$\left( - \frac { \sqrt { 55 } } { 8 } , \frac { 3 } { 8 } \right) \quad$ Find $\cot \mathrm { t }$

Accepted Answer

A)  $- \frac { \sqrt { 55 } } { 3 }$ 
B)  $\frac { \sqrt { 65 } } { 9 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $- \frac { 9 } { 4 }$ 
A)  $- \frac { \sqrt { 55 } } { 3 }$ 
B)  $\frac { \sqrt { 65 } } { 9 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $- \frac { 9 } { 4 }$

Question 16

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\cot 390 ^ { \circ }$

Accepted Answer

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

Question 17

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$
-30° A) $\frac { \pi } { 8 }$

Accepted Answer

B)  $\frac { \pi } { 6 }$ 
C)  $\frac { \pi } { 7 }$ 
D)  $\frac { \pi } { 5 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $\frac { \pi } { 7 }$ 
D)  $\frac { \pi } { 5 }$

Question 18

Graph the function. Show at least one period.
-$$y = 4 \cos \left( - 3 x + \frac { \pi } { 2 } \right)$$
 
 A)

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Find the phase shift of the function.
-$$y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $4 \pi$ units down 
B)  $4 \pi$ units up 
C)  $\frac { \pi } { 8 }$ units to the right 
D)  $\frac { \pi } { 2 }$ units to the left 
A)  $4 \pi$ units down 
B)  $4 \pi$ units up 
C)  $\frac { \pi } { 8 }$ units to the right 
D)  $\frac { \pi } { 2 }$ units to the left

Solve the problem. -What is the $y$ -intercept of $y = \cos x$ ?

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \cos \frac { 1 } { 3 } x \quad$ Find the amplitude.

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\cos x = 0$ ?

Find the exact value of the expression. Do not use a calculator. - $\cos 120 ^ { \circ } \tan 60 ^ { \circ }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quad$ Find $\cos \theta$

Find the exact value. Do not use a calculator. - $\sin \pi$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin 495 ^ { \circ }$

Find the exact value. Do not use a calculator. - $\sin ( 4 \pi )$

Find the exact value. Do not use a calculator. - $\sin 0$

Find the phase shift of the function. - $y = 5 \sin \left( x - \frac { \pi } { 4 } \right)$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( 5,12 )$ Find $\sin \theta$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( - \frac { \sqrt { 55 } } { 8 } , \frac { 3 } { 8 } \right) \quad$ Find $\cot \mathrm { t }$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\cot 390 ^ { \circ }$

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ -30° A) $\frac { \pi } { 8 }$ B) $\frac { \pi } { 6 }$ C) $\frac { \pi } { 7 }$ D) $\frac { \pi } { 5 }$

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

Find the phase shift of the function. - $y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)$

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

Solve the problem. -What is the yyy -intercept of y=cos⁡xy = \cos xy=cosx ?

Without graphing the function, determine its amplitude or period as requested. - y=−4cos⁡13xy = - 4 \cos \frac { 1 } { 3 } x \quady=−4cos31​x Find the amplitude.

Solve the problem. -For what numbers x,0≤x≤2πx , 0 \leq x \leq 2 \pix,0≤x≤2π , does cos⁡x=0\cos x = 0cosx=0 ?

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

Find the exact value of the expression. Do not use a calculator. - cos⁡120∘tan⁡60∘\cos 120 ^ { \circ } \tan 60 ^ { \circ }cos120∘tan60∘

Find the exact value of the indicated trigonometric function of θ\thetaθ - tan⁡θ=−2120,270∘<θ<360∘\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quadtanθ=−2021​,270∘<θ<360∘ Find cos⁡θ\cos \thetacosθ

Find the exact value. Do not use a calculator. - sin⁡π\sin \pisinπ

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - sin⁡495∘\sin 495 ^ { \circ }sin495∘

Find the exact value. Do not use a calculator. - sin⁡(4π)\sin ( 4 \pi )sin(4π)

Find the exact value. Do not use a calculator. - sin⁡0\sin 0sin0

Find the phase shift of the function. - y=5sin⁡(x−π4)y = 5 \sin \left( x - \frac { \pi } { 4 } \right)y=5sin(x−4π​)

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (5,12)( 5,12 )(5,12) Find sin⁡θ\sin \thetasinθ

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - cot⁡390∘\cot 390 ^ { \circ }cot390∘

Convert the angle in degrees to radians. Express the answer as multiple of π.\pi .π. -30° A) π8\frac { \pi } { 8 }8π​ B) π6\frac { \pi } { 6 }6π​ C) π7\frac { \pi } { 7 }7π​ D) π5\frac { \pi } { 5 }5π​

Graph the function. Show at least one period. - y=4cos⁡(−3x+π2)y = 4 \cos \left( - 3 x + \frac { \pi } { 2 } \right)y=4cos(−3x+2π​) A) B) C) D)

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

Find the phase shift of the function. - y=−4sin⁡(4x−π2)y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)y=−4sin(4x−2π​)