Question 1

Find a solution for the equation. Assume that all angles are acute angles.
-sec ϴ = csc(ϴ + 46°)

Accepted Answer

A) 23° 
B) 67° 
C) 22° 
D) 68° 
A) 23° 
B) 67° 
C) 22° 
D) 68°

Question 2

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-cos 47° cos 133° - sin 47° sin 133°

Accepted Answer

A) 2 
B) 0 
C) 1 
D) -1 
A) 2 
B) 0 
C) 1 
D) -1

Question 3

Solve the problem.
-Find a formula for the area of the figure in terms of s.

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }$ 
B)  $\sqrt { 6 } \mathrm {~s} ^ { 2 }$ 
C)  $\frac { \sqrt { 6 } } { 4 } s ^ { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$ 
A)  $\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }$ 
B)  $\sqrt { 6 } \mathrm {~s} ^ { 2 }$ 
C)  $\frac { \sqrt { 6 } } { 4 } s ^ { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$

Question 4

Find a solution for the equation. Assume that all angles are acute angles.
-$\sec \left( \theta + 12 ^ { \circ } \right) = \csc \left( 2 \theta + 15 ^ { \circ } \right)$

Accepted Answer

A)  $23.5 ^ { \circ }$ 
B)  $19 ^ { \circ }$ 
C)  $15 ^ { \circ }$ 
D)  $21 ^ { \circ }$ 
A)  $23.5 ^ { \circ }$ 
B)  $19 ^ { \circ }$ 
C)  $15 ^ { \circ }$ 
D)  $21 ^ { \circ }$

Question 5

Solve the problem.
-The index of refraction for air, Ia, is 1.0003. The index of refraction for water, Iw, is 1.3. If $\frac { \mathrm { I } _ { \mathrm { W } } } { \mathrm { I } _ { \mathrm { a } } } = \frac { \sin \mathrm { A } } { \sin \mathrm { W } }$, and $\mathrm { A } = 31.5 ^ { \circ }$, find $\mathrm { W }$ to the nearest tenth.

Accepted Answer

A)  $22.7 ^ { \circ }$ 
B)  $23.7 ^ { \circ }$ 
C)  $21.7 ^ { \circ }$ 
D)  $20.7 ^ { \circ }$ 
A)  $22.7 ^ { \circ }$ 
B)  $23.7 ^ { \circ }$ 
C)  $21.7 ^ { \circ }$ 
D)  $20.7 ^ { \circ }$

Question 6

Find the exact value of the expression.
-sec (-1215°)

Accepted Answer

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

Question 7

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-tan ϴ = 1.5047547

Accepted Answer

A) 56.3935717° 
B) 123.606428° 
C) 33.6064283° 
D) 236.393572° 
A) 56.3935717° 
B) 123.606428° 
C) 33.6064283° 
D) 236.393572°

Question 8

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-sin 77°

Accepted Answer

A) csc 13° 
B) sin 167° 
C) cos 13° 
D) cos 77° 
A) csc 13° 
B) sin 167° 
C) cos 13° 
D) cos 77°

Question 9

Use a calculator to decide whether the statement is true or false.
-cos (2 ·30°)= 2 · cos 30°

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?

Accepted Answer

A) 4736 km 
B) 492 km 
C) 4710 km 
D) 52 km 
A) 4736 km 
B) 492 km 
C) 4710 km 
D) 52 km

Question 11

Solve the problem.
-Find the exact value of x in the figure.

Accepted Answer

A)  $23 \sqrt { 3 }$ 
B)  $22 \sqrt { 6 }$ 
C)  $22 \sqrt { 3 }$ 
D)  $20 \sqrt { 3 }$ 
A)  $23 \sqrt { 3 }$ 
B)  $22 \sqrt { 6 }$ 
C)  $22 \sqrt { 3 }$ 
D)  $20 \sqrt { 3 }$

Question 12

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 $\sec B$ when $a = 2$ and $b = 9$.

Accepted Answer

A)  $\frac { 2 \sqrt { 85 } } { 85 }$ 
B)  $\frac { 9 \sqrt { 85 } } { 85 }$ 
C)  $\frac { \sqrt { 85 } } { 2 }$ 
D)  $\frac { 2 \sqrt { 85 } } { 9 }$ 
A)  $\frac { 2 \sqrt { 85 } } { 85 }$ 
B)  $\frac { 9 \sqrt { 85 } } { 85 }$ 
C)  $\frac { \sqrt { 85 } } { 2 }$ 
D)  $\frac { 2 \sqrt { 85 } } { 9 }$

Question 13

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 $I$ and the positive $x$-axis is $\frac { \sqrt { 2 } } { 2 }$.

Accepted Answer

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

Question 14

Solve the problem.
-The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ, where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0
For downhill travel). What is the grade resistance (to the nearest pound)of a 2100-lb car traveling
Downhill on a 5° grade (ϴ = -5°)?

Accepted Answer

A) 183 lb 
B) -2105 lb 
C) 2105 lb 
D) -183 lb 
A) 183 lb 
B) -2105 lb 
C) 2105 lb 
D) -183 lb

Question 15

Solve the problem for the given information.
-What angle does the line y = x make with the positive x-axis?

Accepted Answer

A) 90° 
B) 60° 
C) 30° 
D) 45° 
A) 90° 
B) 60° 
C) 30° 
D) 45°

Question 16

Evaluate.
-$3 \cot ^ { 2 } 45 ^ { \circ } + \tan ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }$

Accepted Answer

A)  7 
B)  12 
C)  84 
D)  14 
A)  7 
B)  12 
C)  84 
D)  14

Question 17

Solve the right triangle.
-a = 3.6 m, B = 30.3°, C = 90° Round values to one decimal place.

Accepted Answer

A) A = 59.7°, b = 4.4 m, c = 5.7 m 
B) A = 59.7°, b = 2.1 m, c = 4.2 m 
C) A = 59.7°, b = 1 m, c = 3.7 m 
D) A = 59.7°, b = 4.4 m, c = 4.2 m 
A) A = 59.7°, b = 4.4 m, c = 5.7 m 
B) A = 59.7°, b = 2.1 m, c = 4.2 m 
C) A = 59.7°, b = 1 m, c = 3.7 m 
D) A = 59.7°, b = 4.4 m, c = 4.2 m

Question 18

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

Accepted Answer

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

Question 19

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$\mathrm { a } = 50.26 \mathrm { ft } , \mathrm { c } = 231 \mathrm { ft }$
Round the missing side length to two decimal places.

Accepted Answer

A)  $\mathrm { A } = 13 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 76 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 225.47 \mathrm { ft }$ 
B)  $A = 10 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 79 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 236.74 \mathrm { ft }$ 
C)  $\mathrm { A } = 12 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 77 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 209.69 \mathrm { ft }$ 
D)  $A = 12 ^ { \circ } 34 ^ { \prime } ; B = 77 ^ { \circ } 26 ^ { \prime } ; b = 225.47 \mathrm { ft }$ 
A)  $\mathrm { A } = 13 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 76 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 225.47 \mathrm { ft }$ 
B)  $A = 10 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 79 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 236.74 \mathrm { ft }$ 
C)  $\mathrm { A } = 12 ^ { \circ } 34 ^ { \prime } , \mathrm { B } = 77 ^ { \circ } 26 ^ { \prime } , \mathrm { b } = 209.69 \mathrm { ft }$ 
D)  $A = 12 ^ { \circ } 34 ^ { \prime } ; B = 77 ^ { \circ } 26 ^ { \prime } ; b = 225.47 \mathrm { ft }$

Question 20

Find the exact value of the expression.
-cos 210°

Accepted Answer

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

Find a solution for the equation. Assume that all angles are acute angles. -sec ϴ = csc(ϴ + 46°)

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -cos 47° cos 133° - sin 47° sin 133°

Solve the problem. -Find a formula for the area of the figure in terms of s.

Find a solution for the equation. Assume that all angles are acute angles. - $\sec \left( \theta + 12 ^ { \circ } \right) = \csc \left( 2 \theta + 15 ^ { \circ } \right)$

Find the exact value of the expression. -sec (-1215°)

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -tan ϴ = 1.5047547

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -sin 77°

Use a calculator to decide whether the statement is true or false. -cos (2 ·30°)= 2 · cos 30°

Solve the problem. -An airplane travels at 165 km/h for 3 hr in a direction of 174° from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?

Solve the problem. -Find the exact value of x in the figure.

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 $I$ and the positive $x$ -axis is $\frac { \sqrt { 2 } } { 2 }$ .

Solve the problem for the given information. -What angle does the line y = x make with the positive x-axis?

Evaluate. - $3 \cot ^ { 2 } 45 ^ { \circ } + \tan ^ { 4 } 300 ^ { \circ } - 5 \sin ^ { 4 } 0 ^ { \circ }$

Solve the right triangle. -a = 3.6 m, B = 30.3°, C = 90° Round values to one decimal place.

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

Find the exact value of the expression. -cos 210°

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

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Exam 2: Acute Angles and Right Triangles