AnswersMathematics IIITrigonometric Functions

Trigonometric Functions — Test Answers

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Which function describes the graph shown?

A
y is equal to 2 cosine x minus 1 half
B
y is equal to 1 half sine x minus 2
C
y is equal to 2 sine x minus 1 half
D
y is equal to 1 half cosine x minus 2
2
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What is the equation of the graph?

A
y is equal to cosine of open paren x plus pi close paren
B
y is equal to cosine of open paren x plus pi over 3 close paren
C
y is equal to cosine of open paren x plus pi over 2 close paren
D
y is equal to cosine of open paren x plus 2 pi close paren
3

What is the equation of the given graph?

A
y is equal to secant of x minus 4
B
y is equal to secant of open paren x minus 4 close paren
C
y is equal to secant of open paren x plus 4 close paren plus 4
D
y is equal to secant of open paren x plus 4 close paren minus 4
4

Which function is graphed?

A
f of x is equal to negative cosine times x
B
f of x is equal to negative sine times x
C
f of x is equal to cosine of x
D
f of x is equal to sine of x
5

Which transformations are needed to change the parent cosine function to the cosine function shown in the graph?

A
vertical compression of 2 , horizontal stretch to a period of pi over 4 , phase shift of pi over 4 units to the left, vertical shift of 2 units down
B
vertical stretch of 2 , horizontal stretch to a period of 2 pi , phase shift of pi over 2 units to the right, vertical shift of 1 unit up
C
vertical compression of 2 , horizontal compression to a period of 4 pi , phase shift of pi over 3 units to the left, vertical shift of 1 unit down
D
vertical stretch of 2 , horizontal compression to a period of pi over 2 , phase shift of pi units to the right, vertical shift of 1 unit down
6

Which transformations are needed to change the parent cosine function to y is equal to 3 cosine open paren 10 times open paren x minus pi close paren close paren ?

A
vertical compression of 3 , horizontal stretch to a period of 5 pi , phase shift of pi units to the left
B
vertical stretch of 3 , horizontal compression to a period of pi over 5 , phase shift of pi units to the left
C
vertical stretch of 3 , horizontal compression to a period of pi over 5 , phase shift of pi units to the right
D
vertical compression of 3 , horizontal stretch to a period of 10 pi , phase shift of pi units to the right
7

A circle has a central angle measuring 3 pi over 4 radians that intersects an arc of length 45 in. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3 point 1 4 for pi

A
105 point 6 in.
B
135 point 0 in.
C
2 point 4 in.
D
19 point 1 in.
9

A circle has a central angle of 6 radians that intersects an arc of length 14 in. Which equation finds the length of the radius, r , of the circle?

A
r is equal to 14 sixths
B
r is equal to 6 times 14
C
r is equal to 6 over 14
D
r is equal to 6 plus 14
10

Which of the following is the graph of y is equal to 0 point 5 secant open paren x plus pi over 3 close paren minus 2 ?

A
Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).
B
Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).
C
Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).
D
Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).
11

What is the period of the function y is equal to 3 halves cotangent open paren 3 fifths x close paren plus 5 ?

A
2 pi over 3 units
B
3 pi over 5 units
C
5 pi over 3 units
D
pi over 5 units
12

Which transformations are needed to change the parent cosine function to y is equal to 0 point 3 5 cosine open paren 8 times open paren x minus pi over 4 close paren close paren ?

A
vertical stretch of 0 point 3 5 , horizontal stretch to a period of 16 pi , phase shift of pi over 4 units to the right
B
vertical stretch of 0 point 3 5 , horizontal stretch to a period of pi over 4 , phase shift of pi over 4 units to the right
C
vertical compression of 0 point 3 5 , horizontal compression to a period of 4 pi , phase shift of pi over 4 units to the left
D
vertical compression of 0 point 3 5 , horizontal compression to a period of pi over 4 , phase shift of pi over 4 units to the right
13

Haruto simplified the value. cosecant of open paren 19 pi over 4 close paren is equal to square root of 2 Which statement explains whether Haruto is correct?

A
Haruto is not correct because the angle is coterminal with 3 pi over 4 , and cosecant of open paren 3 pi over 4 close paren is equal to the fraction with numerator negative 1 and denominator square root of 2 is equal to the fraction with numerator negative square root of 2 and denominator 2 .
B
Haruto is not correct because the angle is coterminal with pi over 4 , and cosecant of open paren pi over 4 close paren is equal to the fraction with numerator 1 and denominator square root of 2 is equal to the fraction with numerator square root of 2 and denominator 2 .
C
Haruto is correct because the angle is coterminal with 3 pi over 4 and the reference angle is pi over 4 .
D
Haruto is correct because the angle is coterminal with pi over 4 , which is also the reference angle.
14

A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, theta ?

A
theta is equal to 7 plus 5
B
theta is equal to 7 fifths
C
theta is equal to 5 sevenths
D
theta is equal to 7 times 5
15

What are the period, phase shift, and vertical shift of y is equal to cosecant of open bracket 3 times open paren x plus 4 close paren close bracket plus 6 ?

A
period: pi over 3 ; phase shift: 4 units left; vertical shift: 6 units down
B
period: 2 pi over 3 ; phase shift: 4 units left; vertical shift: 6 units up
C
period: pi over 3 ; phase shift: 4 units right; vertical shift: 6 units up
D
period: 2 pi over 3 ; phase shift: 4 units right; vertical shift: 6 units down
16

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 60 -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 30 -degree reference angle and is located in Quadrant II or III
D
theta has a 30 -degree reference angle and is located in Quadrant II or IV
17

How long is the arc intersected by a central angle of pi over 2 radians in a circle with a radius of 4 point 5 cm? Round your answer to the nearest tenth. Use 3 point 1 4 for pi

A
0 point 3 cm
B
7 point 1 cm
C
0 point 7 cm
D
2 point 9 cm
18

What is 270 degrees converted to radians?

A
3
B
3 halves
C
pi over 6
D
3 pi over 2
19

The point cap p times open paren x comma y close paren is on the terminal ray of angle theta If theta is between pi radians and 3 pi over 2 radians and cosecant theta is equal to negative 5 halves , what are the coordinates of cap p times open paren x comma y close paren ?

A
cap p times open paren negative 2 comma negative square root of 21 close paren
B
cap p times open paren negative square root of 21 comma negative 2 close paren
C
cap p times open paren negative 2 comma square root of 21 close paren
D
cap p times open paren square root of 21 comma negative 2 close paren
20

Which function will have a y -intercept at negative 1 and an amplitude of 2 ?

A
f of x is equal to negative 2 sine x minus 1
B
f of x is equal to negative sine times x minus 1
C
f of x is equal to negative 2 cosine x minus 1
D
f of x is equal to negative cosine times x
21

What is the amplitude of the function?

A
2
B
1
C
2 pi
D
pi

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