AnswersPrecalculusModeling with Trigonometric Expressions and Functions: Part One

Modeling with Trigonometric Expressions and Functions: Part One — Test Answers

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1
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Which equation models this data?

A
y is equal to 6 cosine open paren pi over 12 x minus pi over 3 close paren plus 17
B
y is equal to 6 cosine open paren pi over 12 x minus pi over 4 close paren plus 17
C
y is equal to 3 cosine open paren pi over 12 x minus pi over 4 close paren plus 17
D
y is equal to 3 cosine open paren pi over 12 x minus pi over 3 close paren plus 17
2
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Which function represents the graph?

A
y is equal to 3 sine x
B
y is equal to negative 3 cosine x
C
y is equal to 3 cosine x
D
y is equal to negative 3 sine x
4

Which of the following best explains the value of sine pi over 3 on the given unit circle?

A
sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the vertical distance from the x -axis on the graph.
B
sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the horizontal distance from the y -axis on the graph.
C
sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the horizontal distance from the y -axis on the graph.
D
sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the vertical distance from the x -axis on the graph.
5

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

How many degrees is 15 over 16 pi radians?

A
337.5 degrees
B
93.75 degrees
C
168.75 degrees
D
84.375 degrees
7

Over which interval is the graph of y is equal to cosine of x strictly increasing?

A
0 is less than x comma x is less than pi
B
pi is less than x comma x is less than 2 pi
C
pi over 2 is less than x comma x is less than 3 pi over 2
D
0 is less than x comma x is less than pi over 2
9

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
11

In which quadrant(s) is cosecant of x positive?

A
quadrant II only
B
quadrants I and II
C
quadrant I only
D
quadrants I and III
13

The function g of x represents f of x is equal to 9 cosine open paren x minus pi over 2 close paren plus 3 after translating pi over 6 units left and 4 units up. Which equation represents g of x ?

A
g of x is equal to 9 cosine open paren x minus pi over 3 close paren plus 7
B
g of x is equal to 9 cosine open paren x minus 2 pi over 3 close paren minus 1
C
g of x is equal to 9 cosine open paren x minus pi over 3 close paren minus 1
D
g of x is equal to 9 cosine open paren x minus 2 pi over 3 close paren plus 7
14

Which of the following is true of the location of an angle, theta , whose tangent value is negative the fraction with numerator square root of 3 and denominator 3 ?

A
theta has a 30 -degree reference angle and is located in Quadrant II or IV
B
theta has a 60 -degree reference angle and is located in Quadrant II or III
C
theta has a 60 -degree reference angle and is located in Quadrant II or IV
D
theta has a 30 -degree reference angle and is located in Quadrant II or III
15

If angle cap b measures 25 degrees , what is the approximate perimeter of the triangle? Expand Image

A
25 point 2 units
B
11 point 8 units
C
10 point 3 units
D
22 point 1 units
16

Suppose the function h of x is equal to sine x is translated 3 pi over 2 units left and 11 units down. Which graph represents the result?

A
Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).
B
Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).
C
Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).
D
Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).
17

What is the exact value of cotangent of open paren 3 pi over 4 close paren ?

A
square root of 2
B
1
C
negative square root of 2
D
negative 1
18

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?

A
3 plus 3 square root of 2 ft
B
6 plus 3 square root of 2 ft
C
3 plus 3 square root of 3 ft
D
6 plus 3 square root of 3 ft

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