Question 1

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-cos 164°5´

Accepted Answer

A) -0.5808308 
B) -0.4808308 
C) -0.7616616 
D) -0.9616616 
A) -0.5808308 
B) -0.4808308 
C) -0.7616616 
D) -0.9616616

Question 2

Find the exact value of the expression.
-$\cos 840 ^ { \circ }$

Accepted Answer

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

Question 3

Without using a calculator, give the exact trigonometric function value with rational denominator.
-cos 30°

Accepted Answer

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

Question 4

Without using a calculator, give the exact trigonometric function value with rational denominator.
-csc 45°

Accepted Answer

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

Question 5

Find the reference angle for the given angle.
-388°

Accepted Answer

A) 152° 
B) 28° 
C) 62° 
D) 118° 
A) 152° 
B) 28° 
C) 62° 
D) 118°

Question 6

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an
airplane located at that point. Express the bearing using both methods.
-(0, )

Accepted Answer

A)  $0 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
B)  $180 ^ { \circ } ; \mathrm { N } \mathrm {} 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
C)  $0 ^ { \circ } ; \mathrm { N } \mathrm {} 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
D)  $180 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
A)  $0 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
B)  $180 ^ { \circ } ; \mathrm { N } \mathrm {} 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
C)  $0 ^ { \circ } ; \mathrm { N } \mathrm {} 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
D)  $180 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$

Question 7

Without using a calculator, give the exact trigonometric function value with rational denominator.
-sec 30°

Accepted Answer

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

Question 8

Find all values of , if is in the interval [0, 360°) and has the given function value.
-$$\sin \theta = - \frac { 1 } { 2 }$$

Accepted Answer

A)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$

Question 9

Solve the problem.
-Find h as indicated in the figure. Round to the nearest meter.

Accepted Answer

A)  $165 \mathrm {~m}$ 
B)  $50 \mathrm {~m}$ 
C)  $86 \mathrm {~m}$ 
D)  $65 \mathrm {~m}$ 
A)  $165 \mathrm {~m}$ 
B)  $50 \mathrm {~m}$ 
C)  $86 \mathrm {~m}$ 
D)  $65 \mathrm {~m}$

Question 10

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\sin 30 ^ { \circ }$

Accepted Answer

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

Question 11

Find the sign of the following.
-$\csc ( - \theta )$, given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$.

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 12

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$B = 58.45 ^ { \circ } , a = 434.7 \mathrm {~m}$$
Give side lengths to two decimal places.

Accepted Answer

A)  $A = 31.55 ^ { \circ } ; \mathrm { b } = 707.98 \mathrm {~m} ; \mathrm { c } = 843.43 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 707.98 \mathrm {~m} ; \mathrm { c } = 830.78 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 664.51 \mathrm {~m} ; \mathrm { c } = 830.78 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 751.45 \mathrm {~m} ; \mathrm { c } = 817.21 \mathrm {~m}$ 
A)  $A = 31.55 ^ { \circ } ; \mathrm { b } = 707.98 \mathrm {~m} ; \mathrm { c } = 843.43 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 707.98 \mathrm {~m} ; \mathrm { c } = 830.78 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 664.51 \mathrm {~m} ; \mathrm { c } = 830.78 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 751.45 \mathrm {~m} ; \mathrm { c } = 817.21 \mathrm {~m}$

Question 13

Find the exact value of the expression.
-cs

Accepted Answer

A)  -2 
B)  2 
C)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 3 }$ c 330° 
A)  -2 
B)  2 
C)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 3 }$ c 330°

Question 14

Find the exact value of the expression.
-cot 120°

Accepted Answer

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

Question 15

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $\mathrm { I }$ and the positive $x$-axis is $\frac { \sqrt { 3 } } { 2 }$.

Accepted Answer

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

Question 16

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-cos 33°

Accepted Answer

A) cos 123° 
B) sin 57° 
C) sec 57° 
D) sin 33° 
A) cos 123° 
B) sin 57° 
C) sec 57° 
D) sin 33°

Question 17

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\cot \mathrm { A }$ when $\mathrm { a } = 5$ and $\mathrm { c } = 6$.

Accepted Answer

A)  $\frac { 6 \sqrt { 11 } } { 11 }$ 
B)  $\frac { 5 \sqrt { 11 } } { 11 }$ 
C)  $\frac { \sqrt { 11 } } { 6 }$ 
D)  $\frac { \sqrt { 11 } } { 5 }$ 
A)  $\frac { 6 \sqrt { 11 } } { 11 }$ 
B)  $\frac { 5 \sqrt { 11 } } { 11 }$ 
C)  $\frac { \sqrt { 11 } } { 6 }$ 
D)  $\frac { \sqrt { 11 } } { 5 }$

Question 18

Find the sign of the following.
-$\tan \frac { \theta } { 2 }$, given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$.

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 19

Solve the problem.
-A boat sails for 3 hours at 25 mph in a direction 93°2'. How far south has it sailed (to the nearest mile)?

Accepted Answer

A) 2 mi 
B) 6 mi 
C) 4 mi 
D) 0 mi 
A) 2 mi 
B) 6 mi 
C) 4 mi 
D) 0 mi

Question 20

Find the exact value of the expression.
-$\csc 240 ^ { \circ }$

Accepted Answer

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

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 164°5´

Find the exact value of the expression. - $\cos 840 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. -cos 30°

Without using a calculator, give the exact trigonometric function value with rational denominator. -csc 45°

Find the reference angle for the given angle. -388°

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. -(0, )

Without using a calculator, give the exact trigonometric function value with rational denominator. -sec 30°

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { 1 } { 2 }$

Solve the problem. -Find h as indicated in the figure. Round to the nearest meter.

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sin 30 ^ { \circ }$

Find the sign of the following. - $\csc ( - \theta )$ , given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$ .

Find the exact value of the expression. -cs

Find the exact value of the expression. -cot 120°

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $\mathrm { I }$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -cos 33°

Find the sign of the following. - $\tan \frac { \theta } { 2 }$ , given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$ .

Solve the problem. -A boat sails for 3 hours at 25 mph in a direction 93°2'. How far south has it sailed (to the nearest mile)?

Find the exact value of the expression. - $\csc 240 ^ { \circ }$

Trigonometric Functions

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 2: Acute Angles and Right Triangles