Question 1

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 2

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

Accepted Answer

A)  $y = - 2 \sin ( 3 x )$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = - 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
A)  $y = - 2 \sin ( 3 x )$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = - 2 \sin \left( \frac { 1 } { 3 } x \right)$

Question 3

Use transformations to graph the function.
-$y=-3 \cos x$

Accepted Answer

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

Question 4

Convert the angle to a decimal in degrees. Round the answer to two decimal places.
-297°20'44"

Accepted Answer

A)  $297.35 ^ { \circ }$ 
B)  $297.31 ^ { \circ }$ 
C)  $297.41 ^ { \circ }$ 
D)  $297.36 ^ { \circ }$ 
A)  $297.35 ^ { \circ }$ 
B)  $297.31 ^ { \circ }$ 
C)  $297.41 ^ { \circ }$ 
D)  $297.36 ^ { \circ }$

Question 5

Solve the problem.
-An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?

Accepted Answer

A)  $2 \mathrm {~m} / \mathrm { sec }$ 
B)  $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$ 
C)  $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$ 
D)  $3 \mathrm {~m} / \mathrm { sec }$ 
A)  $2 \mathrm {~m} / \mathrm { sec }$ 
B)  $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$ 
C)  $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$ 
D)  $3 \mathrm {~m} / \mathrm { sec }$

Question 6

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$$\cos \frac { 3 \pi } { 7 }$$

Accepted Answer

A)  0.22 
B)  1.05 
C)  1.00 
D)  0.27 
A)  0.22 
B)  1.05 
C)  1.00 
D)  0.27

Question 7

Find an equation for the graph.
-

Accepted Answer

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

Question 8

Name the quadrant in which the angle θ lies.
-$\sec \theta < 0 , \quad \tan \theta < 0$

Accepted Answer

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

Question 9

Draw the angle.
-$135 ^ { \circ }$

Accepted Answer

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

Question 10

Choose the one alternative that best completes the statement or answers the question.
A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$
Find $\cos \theta$.

Accepted Answer

A)  $- \frac { 34 } { 5 }$ 
B)  $\frac { 5 \sqrt { 34 } } { 34 }$ 
C)  $- \frac { 3 \sqrt { 34 } } { 34 }$ 
D)  $\frac { 34 } { 3 }$ 
A)  $- \frac { 34 } { 5 }$ 
B)  $\frac { 5 \sqrt { 34 } } { 34 }$ 
C)  $- \frac { 3 \sqrt { 34 } } { 34 }$ 
D)  $\frac { 34 } { 3 }$

Question 11

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$\theta = 60 ^ { \circ } , \mathrm { A } = 100$ square meters, $\mathrm { r } =$ ?

Accepted Answer

A)  $6.26 \mathrm {~m}$ 
B)  $39.25 \mathrm {~m}$ 
C)  $157 \mathrm {~m}$ 
D)  $13.82 \mathrm {~m}$ 
A)  $6.26 \mathrm {~m}$ 
B)  $39.25 \mathrm {~m}$ 
C)  $157 \mathrm {~m}$ 
D)  $13.82 \mathrm {~m}$

Question 12

Solve the problem.
-The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The restoring force F, in Newtons, acting on a string pendulum is given by the formula
F = mg sinθ
Where m is the mass in kilograms of the pendulum's bob, g =9.8 meters per second per second is the acceleration
Due to gravity, and θ is angle at which the pendulum is displaced from the perpendicular. What is the value of
The restoring force when m = 0.8 kilogram and θ = 60°? If necessary, round the answer to the nearest tenth of a
Newton.

Accepted Answer

A)  6.9 N 
B)  6.8 N 
C)  2.4 N 
D)  3.9 N 
A)  6.9 N 
B)  6.8 N 
C)  2.4 N 
D)  3.9 N

Question 13

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

Accepted Answer

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

Question 14

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 15

Write the equation of a sine function that has the given characteristics.
-Amplitude: 5
Period: 3

Accepted Answer

A)  $y = 4 \sin ( 3 x )$ 
B)  $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 2 } \pi x \right)$ 
D)  $y = \sin ( 3 \pi x ) + 4$ 
A)  $y = 4 \sin ( 3 x )$ 
B)  $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$ 
C)  $y = 3 \sin \left( \frac { 1 } { 2 } \pi x \right)$ 
D)  $y = \sin ( 3 \pi x ) + 4$

Question 16

Write the word or phrase that best completes each statement or answers the question.
-The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is $$I = 30 \sin ( 50 \pi t )$$ What is the amplitude? What is the period?
Graph this function over two periods beginning at t = 0.

Accepted Answer

None

Question 17

Graph the function.
-$$\mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 18

Convert the angle in radians to degrees.
-$$\frac { \pi } { 5 }$$

Accepted Answer

A)  $45 ^ { \circ }$ 
B)  $4 ^ { \circ }$ 
C)  $1 ^ { \circ }$ 
D)  $45 \pi ^ { \circ }$ 
A)  $45 ^ { \circ }$ 
B)  $4 ^ { \circ }$ 
C)  $1 ^ { \circ }$ 
D)  $45 \pi ^ { \circ }$

Question 19

Choose the one alternative that best completes the statement or answers the question.
-If $\tan \theta = - 4.5$, find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$.

Accepted Answer

A)  $- 11.5$ 
B)  $- 13.5 + 3 \pi$ 
C)  $- 13.5$ 
D)  undefined 
A)  $- 11.5$ 
B)  $- 13.5 + 3 \pi$ 
C)  $- 13.5$ 
D)  undefined

Question 20

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\sec \frac { \pi } { 12 }$

Accepted Answer

A)  1.00 
B)  0.94 
C)  1.04 
D)  0.98 
A)  1.00 
B)  0.94 
C)  1.04 
D)  0.98

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

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

Use transformations to graph the function. - $y=-3 \cos x$ $Use transformations to graph the function. - y=-3 \cos x$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. -297°20'44"

Solve the problem. -An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos \frac { 3 \pi } { 7 }$

Find an equation for the graph. -

Name the quadrant in which the angle θ lies. - $\sec \theta < 0 , \quad \tan \theta < 0$

Draw the angle. - $135 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$ Find $\cos \theta$ .

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = 60 ^ { \circ } , \mathrm { A } = 100$ square meters, $\mathrm { r } =$ ?

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

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 5 Period: 3

Graph the function. - $\mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)$ $Graph the function. - \mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)$

Convert the angle in radians to degrees. - $\frac { \pi } { 5 }$

Choose the one alternative that best completes the statement or answers the question. -If $\tan \theta = - 4.5$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sec \frac { \pi } { 12 }$

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 5: Trigonometric Functions

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

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

Use transformations to graph the function. - y=−3cos⁡xy=-3 \cos xy=−3cosx

Convert the angle to a decimal in degrees. Round the answer to two decimal places. -297°20'44"

Solve the problem. -An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cos⁡3π7\cos \frac { 3 \pi } { 7 }cos73π​

Find an equation for the graph. -

Name the quadrant in which the angle θ lies. - sec⁡θ<0,tan⁡θ<0\sec \theta < 0 , \quad \tan \theta < 0secθ<0,tanθ<0

Draw the angle. - 135∘135 ^ { \circ }135∘

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - θ=60∘,A=100\theta = 60 ^ { \circ } , \mathrm { A } = 100θ=60∘,A=100 square meters, r=\mathrm { r } =r= ?

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

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 5 Period: 3

Graph the function. - y=13cot⁡(x−π4)\mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)y=31​cot(x−4π​)

Convert the angle in radians to degrees. - π5\frac { \pi } { 5 }5π​

Choose the one alternative that best completes the statement or answers the question. -If tan⁡θ=−4.5\tan \theta = - 4.5tanθ=−4.5 , find the value of tan⁡θ+tan⁡(θ+π)+tan⁡(θ+2π)\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )tanθ+tan(θ+π)+tan(θ+2π) .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - sec⁡π12\sec \frac { \pi } { 12 }sec12π​

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Use transformations to graph the function. - $y=-3 \cos x$ $Use transformations to graph the function. - y=-3 \cos x$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos \frac { 3 \pi } { 7 }$

Name the quadrant in which the angle θ lies. - $\sec \theta < 0 , \quad \tan \theta < 0$

Draw the angle. - $135 ^ { \circ }$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\theta = 60 ^ { \circ } , \mathrm { A } = 100$ square meters, $\mathrm { r } =$ ?

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

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

Graph the function. - $\mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)$ $Graph the function. - \mathrm { y } = \frac { 1 } { 3 } \cot \left( \mathrm { x } - \frac { \pi } { 4 } \right)$

Convert the angle in radians to degrees. - $\frac { \pi } { 5 }$

Choose the one alternative that best completes the statement or answers the question. -If $\tan \theta = - 4.5$ , find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sec \frac { \pi } { 12 }$