AnswersMathematics IIITrigonometry of General Triangles and Trigonometric Functions

Trigonometry of General Triangles and Trigonometric Functions — Test Answers

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Which equation correctly uses the law of cosines to solve for y ?

A
y squared is equal to 9 squared plus 19 squared minus 2 9 19 cosine open paren 41 degrees close paren
B
9 squared is equal to y squared plus 19 squared minus 2 y 19 cosine open paren 41 degrees close paren
C
y squared is equal to 9 squared plus 19 squared minus 2 y 19 cosine open paren 41 degrees close paren
D
9 squared is equal to y squared plus 19 squared minus 2 9 19 cosine open paren 41 degrees close paren
2
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What is the measure of angle cap n to the nearest whole degree?

A
45 degrees
B
55 degrees
C
65 degrees
D
35 degrees
3

Consider the relationship, given pi over 2 is less than theta comma theta is less than pi sine squared theta plus cosine squared theta is equal to 1 Which of the following best explains how this relationship and the value of sine theta can be used to find the other trigonometric values?

A
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1 , which can then be used to find all other values.
B
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of negative 1 , since theta is in Quadrant II; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.
C
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of 1 ; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.
D
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
4

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h , the height in feet of the end of one blade, as a function of time, t , in seconds? Assume that the blade is pointing to the right, parallel to the ground at t is equal to 0 seconds, and that the windmill turns counterclockwise at a constant rate.

A
h is equal to negative 10 sine pi t plus 35
B
h is equal to 10 sine open paren pi over 15 t close paren plus 35
C
h is equal to 10 sine pi t plus 35
D
h is equal to negative 10 sine open paren pi over 15 t close paren plus 35
5

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute . Write a sine model, y is equal to A sine b t plus k , for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t is equal to 0 and that the windmill turns counterclockwise at a constant rate.

A
y is equal to 30 sine open paren pi over 15 t close paren plus 30
B
y is equal to 10 sine open paren pi over 15 t close paren plus 10
C
y is equal to 10 sine open paren pi over 15 t close paren plus 30
D
y is equal to 30 sine open paren pi over 15 t close paren plus 10
6

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

A
0 point 4 radian
B
2 point 7 radians
C
1 point 0 radian
D
5 point 0 radians
7

Law of sines: sine of cap A over A is equal to sine of cap b over b is equal to sine of cap c over c Triangle ABC has measures A is equal to 2 , b is equal to 2 , and m angle cap A is equal to 30 degrees What is the measure of angle cap b ?

A
45 degrees
B
15 degrees
C
30 degrees
D
60 degrees
8

An angle measuring 468 n degrees is in standard position. For which value of n will the terminal side fall on the x -axis?

A
n is equal to 5
B
n is equal to 7
C
n is equal to 6
D
n is equal to 4
9

Angle cap d has a measure between 0 degrees and 360 degrees and is coterminal with a negative 920 degrees angle. What is the measure of angle cap d ?

A
160 degrees
B
165 degrees
C
170 degrees
D
155 degrees
10

Which is the graph of y is equal to cosine of x plus 3 ?

A
Image with description A coordinate plane. The graph starts and rises to (0 comma 6). It starts to fall through (pi over 2 comma 3) to (pi comma 0). It then rises through (3 pi over 2 comma 3) to (2 pi comma 6).
B
Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 6 to 2. The wave reaches a maximum at (0 comma negative 2), drops to a minimum at (pi comma negative 4), and rises again to a maximum at (2 pi comma negative 2).
C
Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 2 to 6. The wave reaches a maximum at (0 comma 4), drops to a minimum at (pi comma 2), and rises again to a maximum at (2 pi comma 4).
D
Image with description A line graph on a Cartesian coordinate plane shows a periodic wave function. The x-axis is labeled x with marked points at pi and 2 pi, and the y-axis is labeled y with values from negative 4 to 4. The wave reaches a maximum at (0 comma 3), drops to a minimum at (pi comma negative 3), and rises again to a maximum at (2 pi comma 3).
11

Which of the following are in the correct order from least to greatest?

A
38 degrees , pi over 4 , 80 degrees , 7 pi over 6 , 2 pi
B
38 degrees , 80 degrees , pi over 4 , 7 pi over 6 , 2 pi
C
2 pi , 7 pi over 6 , 80 degrees , pi over 4 , 38 degrees
D
2 pi , 38 degrees , 80 degrees , pi over 4 , 7 pi over 6
12

What is the range of y is equal to negative 3 sine x minus 4 ?

A
all real numbers negative 1 is less than or equal to y comma y is less than or equal to 1
B
all real numbers negative 7 is less than or equal to y comma y is less than or equal to negative 1
C
all real numbers negative 5 is less than or equal to y comma y is less than or equal to 3
D
all real numbers negative 7 is less than or equal to y comma y is less than or equal to 7
13

If cosine theta almost equal to 0 point 3 0 9 0 , which of the following represents approximate values of sine theta and tangent theta , for 0 degrees is less than theta comma theta is less than 90 degrees ?

A
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 0 point 3 2 4 9
B
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 10 point 4 7 3 1
C
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 3 point 0 7 8 0
D
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 0 point 0 9 5 5
14

The angle measures associated with which set of ordered pairs share the same reference angle?

A
open paren negative the fraction with numerator square root of 3 and denominator 2 comma negative 1 half close paren , open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren
B
open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
C
open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
D
open paren 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren negative the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren
15

What is the area of triangle DFG ? Round to the nearest whole square unit.

A
27 square units
B
364 square units
C
38 square units
D
728 square units
16

Which of the following could be the measure of the angle?

A
140 degrees
B
negative 180 degrees
C
510 degrees
D
negative 120 degrees
17

Which equation can be used to solve for angle cap A ?

A
sine of cap A over 4 point 6 is equal to sine of open paren 110 degrees close paren over 3 point 2
B
sine of cap A over 2 point 4 is equal to sine of open paren 110 degrees close paren over 4 point 6
C
sine of cap A over 4 point 6 is equal to sine of open paren 110 degrees close paren over 2 point 4
D
sine of cap A over 3 point 2 is equal to sine of open paren 110 degrees close paren over 4 point 6
18

Which measures are accurate regarding triangle JKL ? Choose two correct answers.

A
k almost equal to 3 point 7 units
B
KL almost equal to 2 point 5 units
C
m angle cap k is equal to 94 degrees
D
KL almost equal to 3 point 2 units
E
k almost equal to 4 point 6 units
19

Find the measure of angle cap q , the smallest angle in a triangle whose sides have lengths 4 , 5 , and 6 Round the measure to the nearest whole degree.

A
56 degrees
B
51 degrees
C
34 degrees
D
41 degrees
20

What are the values of m and theta in the given diagram?

A
m is equal to the fraction with numerator square root of 3 and denominator 3 , theta is equal to pi over 6
B
m is equal to the fraction with numerator square root of 3 and denominator 2 , theta is equal to pi over 6
C
m is equal to the fraction with numerator square root of 3 and denominator 3 , theta is equal to pi over 3
D
m is equal to the fraction with numerator square root of 3 and denominator 2 , theta is equal to pi over 3

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