Question 1

Draw the angle.
-$$- \frac { 3 \pi } { 4 }$$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find the exact value. Do not use a calculator.
-$\sec \frac { \pi } { 3 }$

Accepted Answer

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

Question 4

Draw the angle.
-60° A)

Accepted Answer

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

Question 5

Solve the problem.
-Before exercising, an athlete measures her air flow and obtains $a = 0.65 \sin \left( \frac { 2 \pi } { 5 } t \right)$ where a is measured in liters per second and t is the time in seconds. If a > 0, the athlete is inhaling; if a < 0, the athlete
is exhaling. The time to complete one complete inhalation/exhalation sequence is a respiratory cycle.
What is the amplitude? What is the period? What is the respiratory cycle?
Graph a over two periods beginning at t = 0.

Accepted Answer

None

Question 6

Find the exact value of the expression if θ = 45°. Do not use a calculator.
-$f ( \theta ) = \sin \theta \quad$ Find $3 f ( \theta )$.

Accepted Answer

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

Question 7

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.
-$\mathrm { r } = 9$ feet, $\mathrm { A } = 39$ square feet, $\theta =$ ?

Accepted Answer

A)  $0.48$ radians 
B)  3,159 radians 
C)  $0.96$ radians 
D)  $1,579.5$ radians 
A)  $0.48$ radians 
B)  3,159 radians 
C)  $0.96$ radians 
D)  $1,579.5$ radians

Question 8

Convert the angle to D° M' S'' form. Round the answer to the nearest second.
-$64.64 ^ { \circ }$

Accepted Answer

A)  $64 ^ { \circ } 38 ^ { \prime } 30 ^ { \prime \prime }$ 
B)  $64 ^ { \circ } 38 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $64 ^ { \circ } 38 ^ { \prime } 64 ^ { \prime \prime }$ 
D)  $64 ^ { \circ } 38 ^ { \prime } 24 ^ { \prime \prime }$ 
A)  $64 ^ { \circ } 38 ^ { \prime } 30 ^ { \prime \prime }$ 
B)  $64 ^ { \circ } 38 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $64 ^ { \circ } 38 ^ { \prime } 64 ^ { \prime \prime }$ 
D)  $64 ^ { \circ } 38 ^ { \prime } 24 ^ { \prime \prime }$

Question 9

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 10

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 4 , - 3 ) \quad$ Find $\cos \theta$.

Accepted Answer

A)  $\frac { 4 } { 5 }$ 
B)  $- \frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $- \frac { 3 } { 5 }$ 
A)  $\frac { 4 } { 5 }$ 
B)  $- \frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $- \frac { 3 } { 5 }$

Question 11

Solve the problem.
-For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60°. Round to the nearest hundredth.

Accepted Answer

A)  4.25 ft 
B)  4.40 ft 
C)  4.19 ft 
D)  4.35 ft 
A)  4.25 ft 
B)  4.40 ft 
C)  4.19 ft 
D)  4.35 ft

Question 12

Find the exact value. Do not use a calculator.
-$\tan 45 ^ { \circ }$

Accepted Answer

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

Question 13

Match the function to its graph.
-$$y = - \tan \left( x - \frac { \pi } { 2 } \right)$$

Accepted Answer

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

Question 14

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$g ( \theta ) = \cos \theta \quad$ Find $g ( 2 \theta )$.

Accepted Answer

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

Question 15

Find the exact value of the expression. Do not use a calculator.
-$$\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$$

Accepted Answer

A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 2 }$ 
D)  $\frac { 2 \sqrt { 2 } + 1 } { 6 }$ 
A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 2 }$ 
D)  $\frac { 2 \sqrt { 2 } + 1 } { 6 }$

Question 16

Solve the problem.
-A ship in the Atlantic Ocean measures its position to be 30°48' north latitude. Another ship is reported to be due north of the first ship at 41°17' north latitude. Approximately how far apart are the two ships? Round to the
Nearest mile. Assume that the radius of the Earth is 3960 miles.

Accepted Answer

A)  725 mi 
B)  75,966 mi 
C)  75,991 mi 
D)  1,351 mi 
A)  725 mi 
B)  75,966 mi 
C)  75,991 mi 
D)  1,351 mi

Question 17

Solve the problem.
-The Earth rotates about its pole once every 24 hours. The distance from the pole to a location on Earth 35° north latitude is about 3,243.8 miles. Therefore, a location on Earth at 35° north latitude is spinning on a circle of
Radius 3,243.8 miles. Compute the linear speed on the surface of the Earth at 35° north latitude.

Accepted Answer

A)  135 mph 
B)  20,381 mph 
C)  795 mph 
D)  849 mph 
A)  135 mph 
B)  20,381 mph 
C)  795 mph 
D)  849 mph

Question 18

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.
-$\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad$ Find $\cos t$

Accepted Answer

A)  $- \frac { \sqrt { 39 } } { 5 }$ 
B)  $\frac { 5 } { 8 }$ 
C)  $- \frac { 8 \sqrt { 39 } } { 39 }$ 
D)  $- \frac { \sqrt { 39 } } { 8 }$ 
A)  $- \frac { \sqrt { 39 } } { 5 }$ 
B)  $\frac { 5 } { 8 }$ 
C)  $- \frac { 8 \sqrt { 39 } } { 39 }$ 
D)  $- \frac { \sqrt { 39 } } { 8 }$

Question 19

Solve the problem.
-A mass hangs from a spring which oscillates up and down. The position P of the mass at time t is given by $$\mathrm { P } = 4 \cos ( 4 \mathrm { t } )$$ What is the amplitude? What is the period?
Graph this function over two periods beginning at t = 0.

Accepted Answer

The answer of Solve the problem.
-A mass hangs from a...

Question 20

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\tan \left( - 30 ^ { \circ } \right)$

Accepted Answer

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

Draw the angle. - $- \frac { 3 \pi } { 4 }$

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

Find the exact value. Do not use a calculator. - $\sec \frac { \pi } { 3 }$

Draw the angle. -60° A) B) C) D)

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $f ( \theta ) = \sin \theta \quad$ Find $3 f ( \theta )$ .

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. - $\mathrm { r } = 9$ feet, $\mathrm { A } = 39$ square feet, $\theta =$ ?

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $64.64 ^ { \circ }$

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

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( 4 , - 3 ) \quad$ Find $\cos \theta$ .

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of 60°. Round to the nearest hundredth.

Find the exact value. Do not use a calculator. - $\tan 45 ^ { \circ }$

Match the function to its graph. - $y = - \tan \left( x - \frac { \pi } { 2 } \right)$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $g ( 2 \theta )$ .

Find the exact value of the expression. Do not use a calculator. - $\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$

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. - $\left( - \frac { \sqrt { 39 } } { 8 } , \frac { 5 } { 8 } \right) \quad$ Find $\cos t$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\tan \left( - 30 ^ { \circ } \right)$

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

Draw the angle. - −3π4- \frac { 3 \pi } { 4 }−43π​

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

Find the exact value. Do not use a calculator. - sec⁡π3\sec \frac { \pi } { 3 }sec3π​