Question 1

Find the exact value. Do not use a calculator.
-$\sec 30 ^ { \circ }$

Accepted Answer

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

Question 2

Use transformations to graph the function.
-$$y = \cos \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 3

Solve the problem.
-The path of a projectile fired at an inclination θ to the horizontal with an initial speed vo is a parabola. The range R of the projectile, the horizontal distance that the projectile travels, is found by the formula
Feet per second per second or g = 9.8 meters per second per second. Find the $\mathrm { R } = \frac { \mathrm { v } _ { \mathrm { O } } ^ { 2 } \sin 2 \theta } { \mathrm { g } } \text { where } \mathrm { g } = 32.2$ range of a projectile fired with an initial velocity of 174 feet per second at an angle of 35° to the horizontal.
Round your answer to two decimal places.

Accepted Answer

A)  883.54 ft 
B)  883.44 ft 
C)  1,078.61 ft 
D)  539.30 ft 
A)  883.54 ft 
B)  883.44 ft 
C)  1,078.61 ft 
D)  539.30 ft

Question 4

Solve the problem.
-What is the range of the sine function?

Accepted Answer

A)  all real numbers greater than or equal to 1 or less than or equal to -1 
B)  all real numbers greater than or equal to 0 
C)  all real numbers 
D)  all real numbers from -1 to 1, inclusive 
A)  all real numbers greater than or equal to 1 or less than or equal to -1 
B)  all real numbers greater than or equal to 0 
C)  all real numbers 
D)  all real numbers from -1 to 1, inclusive

Question 5

Find the phase shift of the function.
-$$y = - 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 5 }$ units to the left 
B)  $\pi$ units to the right 
C)  $\frac { \pi } { 4 }$ units to the left 
D)  $\frac { \pi } { 2 }$ units to the right 
A)  $\frac { \pi } { 5 }$ units to the left 
B)  $\pi$ units to the right 
C)  $\frac { \pi } { 4 }$ units to the left 
D)  $\frac { \pi } { 2 }$ units to the right

Question 6

Find the exact value of the indicated trigonometric function of θ.
-$\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$

Accepted Answer

A)  $- \frac { 20 } { 21 }$ 
B)  $- \frac { 21 \sqrt { 2 } } { 4 }$ 
C)  $- \frac { 21 } { 20 }$ 
D)  $\frac { 29 } { 20 }$ 
A)  $- \frac { 20 } { 21 }$ 
B)  $- \frac { 21 \sqrt { 2 } } { 4 }$ 
C)  $- \frac { 21 } { 20 }$ 
D)  $\frac { 29 } { 20 }$

Question 7

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.
-$( - 3 , - 2 ) \quad$ Find $\cot \theta$.

Accepted Answer

A)  $\frac { \sqrt { 13 } } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $- \frac { \sqrt { 13 } } { 3 }$ 
A)  $\frac { \sqrt { 13 } } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $- \frac { \sqrt { 13 } } { 3 }$

Question 8

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.
-$\left( - \frac { \sqrt { 21 } } { 5 } , - \frac { 2 } { 5 } \right)$ Find cot $t$

Accepted Answer

A)  $- \frac { \sqrt { 21 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $- \frac { 2 \sqrt { 21 } } { 21 }$ 
D)  $\frac { \sqrt { 21 } } { 5 }$ 
A)  $- \frac { \sqrt { 21 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $- \frac { 2 \sqrt { 21 } } { 21 }$ 
D)  $\frac { \sqrt { 21 } } { 5 }$

Question 9

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 = 31°? If necessary, round the answer to the nearest tenth of a
Newton.

Accepted Answer

A)  3.2 N 
B)  3.8 N 
C)  6.7 N 
D)  4 N 
A)  3.2 N 
B)  3.8 N 
C)  6.7 N 
D)  4 N

Question 10

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

Accepted Answer

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

Question 11

Write the word or phrase that best completes each statement or answers the question.
-ble. $$\begin{array}{l}
\text { The four Galilean moons of Jupiter have orbital periods and mean distances from Jupiter given by the following }\
\begin{array} { l | c | c } 
& \text { Distance } ( \mathrm { km } ) & \text { Period (Earth hours) } \
\hline \text { Io } & 4.214 \times 10 ^ { 5 } & 42.460 \
\text { Europa } & 6.709 \times 10 ^ { 5 } & 85.243 \
\text { Ganymeade } & 1.070 \times 10 ^ { 6 } & 171.709 \
\text { Callisto } & 1.883 \times 10 ^ { 6 } & 400.536
\end{array}
\end{array}$$ Find the linear speed of each moon. Which is the fastest (in terms of linear speed)?

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

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.
-$\left( \frac { 4 } { 7 } , - \frac { \sqrt { 33 } } { 7 } \right)$ Find $\cos \mathrm { t } .$

Accepted Answer

A)  $\frac { \sqrt { 33 } } { 7 }$ 
B)  $- \frac { \sqrt { 33 } } { 7 }$ 
C)  $- \frac { 4 } { 7 }$ 
D)  $\frac { 4 } { 7 }$ 
A)  $\frac { \sqrt { 33 } } { 7 }$ 
B)  $- \frac { \sqrt { 33 } } { 7 }$ 
C)  $- \frac { 4 } { 7 }$ 
D)  $\frac { 4 } { 7 }$

Question 13

Find the exact value of the expression. Do not use a calculator.
-$\sin 135 ^ { \circ } - \sin 270 ^ { \circ }$

Accepted Answer

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

Question 14

Solve the problem.
-For what numbers $x , 0 \leq x \leq 2 \pi$, does $\cos x = 1$ ?

Accepted Answer

A)  $0,2 \pi$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  none 
A)  $0,2 \pi$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  none

Question 15

Use transformations to graph the function.
-$$y = - 3 \cos \left( x - \frac { \pi } { 2 } \right)$$

Accepted Answer

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

Question 16

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

Accepted Answer

A)  $6.944 \mathrm { yd } ^ { 2 }$ 
B)  $2.182 \mathrm { yd } ^ { 2 }$ 
C)  $21.817 \mathrm { yd } ^ { 2 }$ 
D)  $43.633 \mathrm { yd } ^ { 2 }$ 
A)  $6.944 \mathrm { yd } ^ { 2 }$ 
B)  $2.182 \mathrm { yd } ^ { 2 }$ 
C)  $21.817 \mathrm { yd } ^ { 2 }$ 
D)  $43.633 \mathrm { yd } ^ { 2 }$

Question 17

Graph the function.
-$$y = \tan \left( x - \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 18

Solve the problem.
-For what numbers $x , 0 \leq x \leq 2 \pi$, does $\cos x = - 1$ ?

Accepted Answer

A)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\pi$ 
D)  none 
A)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\pi$ 
D)  none

Question 19

Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\sin \left( - 120 ^ { \circ } \right)$

Accepted Answer

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

Question 20

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

Accepted Answer

A)  $10.996 \mathrm { yd }$ 
B)  $5.498 \mathrm { yd }$ 
C)  $1.795 \mathrm { yd }$ 
D)  $8.913 \mathrm { yd }$ 
A)  $10.996 \mathrm { yd }$ 
B)  $5.498 \mathrm { yd }$ 
C)  $1.795 \mathrm { yd }$ 
D)  $8.913 \mathrm { yd }$

Find the exact value. Do not use a calculator. - $\sec 30 ^ { \circ }$

Use transformations to graph the function. - $y = \cos \left( x + \frac { \pi } { 4 } \right)$ $Use transformations to graph the function. - y = \cos \left( x + \frac { \pi } { 4 } \right)$

Solve the problem. -What is the range of the sine function?

Find the phase shift of the function. - $y = - 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)$

Find the exact value of the indicated trigonometric function of θ. - $\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$

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. - $( - 3 , - 2 ) \quad$ Find $\cot \theta$ .

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. - $\left( - \frac { \sqrt { 21 } } { 5 } , - \frac { 2 } { 5 } \right)$ Find cot $t$

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

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. - $\left( \frac { 4 } { 7 } , - \frac { \sqrt { 33 } } { 7 } \right)$ Find $\cos \mathrm { t } .$

Find the exact value of the expression. Do not use a calculator. - $\sin 135 ^ { \circ } - \sin 270 ^ { \circ }$

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\cos x = 1$ ?

Use transformations to graph the function. - $y = - 3 \cos \left( x - \frac { \pi } { 2 } \right)$ $Use transformations to graph the function. - y = - 3 \cos \left( x - \frac { \pi } { 2 } \right)$

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

Graph the function. - $y = \tan \left( x - \frac { \pi } { 4 } \right)$ $Graph the function. - y = \tan \left( x - \frac { \pi } { 4 } \right)$

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\cos x = - 1$ ?

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 120 ^ { \circ } \right)$

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

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

Find the exact value. Do not use a calculator. - sec⁡30∘\sec 30 ^ { \circ }sec30∘

Use transformations to graph the function. - y=cos⁡(x+π4)y = \cos \left( x + \frac { \pi } { 4 } \right)y=cos(x+4π​)