AnswersMathematics IIITrigonometric Functions

Practice Test Answers

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1
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Which transformations are needed to change the parent sine function to the sine function shown in the graph?

A
vertical stretch of 2 , horizontal compression to a period of 4 pi , vertical shift of 2 units up, phase shift of pi units left
B
vertical compression of 1 half , horizontal stretch to a period of 2 pi , vertical shift of 1 unit down, phase shift of pi units left
C
vertical stretch of 1 half , horizontal compression to a period of 2 pi , vertical shift of 1 unit up, phase shift of pi units left
D
vertical compression of 1 half , horizontal stretch to a period of 4 pi , vertical shift of 1 unit up, phase shift of pi units left
2
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Which of the following is cotangent of theta secant of theta in simplified form?

A
negative 1
B
tangent theta
C
cosecant theta
D
1
3

Which values for theta have the same reference angles?

A
pi over 4 , 3 pi over 4 , 7 pi over 4
B
pi over 6 , pi over 3 , 5 pi over 6
C
pi over 2 , 5 pi over 4 , 7 pi over 4
D
pi over 3 , 5 pi over 6 , 4 pi over 3
5

What is the domain of the function y is equal to tangent of open paren x over 8 close paren ?

A
all real numbers except 8 pi plus 4 n pi , where n is any integer
B
all real numbers except 8 pi plus 8 n pi , where n is any integer
C
all real numbers except 4 pi plus 4 n pi , where n is any integer
D
all real numbers except 4 pi plus 8 n pi , where n is any integer
6

Which of the following is true for f of x is equal to negative 2 sine x minus 3 ?

A
The period of the function is 4 pi .
B
The graph of the function is the graph of f of x is equal to negative 2 sine x shifted 3 units up.
C
The amplitude of the function is 2 .
D
The range of the function is the set of real numbers negative 2 is less than or equal to y comma y is less than or equal to 2 .
7

How long is the arc intersected by a central angle of pi over 3 radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3 point 1 4 for pi

A
1 point 0 ft
B
7 point 0 ft
C
6 point 3 ft
D
5 point 7 ft
8

Which formula gives the zeros of y is equal to sine of x ?

A
k pi over 2 for any positive integer k
B
k pi for any integer k
C
k pi for any positive integer k
D
k pi over 2 for any integer k
9

Which of the following is the graph of y is equal to sine of open paren 4 times open paren x minus pi close paren close paren ?

A
Image with description A coordinate plane. The graph starts and falls to (negative pi comma negative 3). It rises through (negative 3 pi over 4 comma negative 1) to (negative pi over 2 comma 1). It then falls through (negative pi over 4 comma negative 1) to (0 comma negative 3). It then rises through (pi over 4 comma negative 1) to (pi over 2 comma 1). It then falls through (3 pi over 4 comma negative 1) to (pi comma negative 3).
B
Image with description A coordinate plane. The graph starts and rises to (negative 2 pi comma 1). It starts to fall through (negative 7 pi over 4 comma 0) to (negative 3 pi over 2 comma negative 1). It then rises through (negative 5 pi over 4 comma 0) to (negative pi comma 1). It then falls through (negative 3 pi over 4 comma 0) to (negative pi over 2 comma negative 1). It then rises through (negative pi over 4 comma 0) to (0 comma 1). It then falls through (pi over 4 comma 0) to (pi over 2 comma negative 1). It then rises through (3 pi over 4 comma 0) to (pi comma 1). It then falls through (5 pi over 4 comma 0) to (3 pi over 2 comma negative 1). It then rises through (7 pi over 4 comma 0) to (2 pi comma 1).
C
Image with description A coordinate plane. The graph starts and rises to (negative 4 pi comma 1). It starts to fall through (negative 3 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (negative pi comma 0) to (0 comma 1). It then falls through (pi comma 0) to (2 pi comma negative 1). It then rises through (3 pi comma 0) to (4 pi comma 1).
D
Image with description A coordinate plane. The graph starts and rises to (0 comma 1). It falls through (pi over 8 comma negative 1) to (pi over 4 comma negative 3). It then rises through (3 pi over 8 comma negative 1) to (pi over 2 comma 1). It then falls through (5 pi over 8 comma negative 1) to (3 pi over 4 comma negative 3). It then rises through (7 pi over 8 comma negative 1) to (pi comma 1). It then falls through (9 pi over 8 comma negative 1) to (5 pi over 4 comma negative 3). It then rises through (11 pi over 8 comma negative 1) to (3 pi over 2 comma 1). It then falls through (13 pi over 8 comma negative 1) to (7 pi over 4 comma negative 3). It then rises through (15 pi over 8 comma negative 1) to (2 pi comma 1).
10

Melanie simplified the expression the fraction with numerator cotangent of x and denominator open paren 1 over secant of x close paren as shown. Step 1: the fraction with numerator open paren cosine of x over sine of x close paren and denominator cosine of x Step 2: cosine of x over sine of x times 1 over cosine of x Step 3: 1 over sine of x Step 4: tangent of x In which step did Melanie make the first error, and which expression should she have written in that step?

A
step 1; the fraction with numerator open paren sine of x over cosine of x close paren and denominator cosine of x
B
step 4; cosecant of x
C
step 1; the fraction with numerator open paren cosine of x over sine of x close paren and denominator sine of x
D
step 4; cosine of x
11

Which point does the graph of the parent function y is equal to tangent of x pass through?

A
open paren pi over 3 comma square root of 3 close paren
B
open paren square root of 3 comma pi over 3 close paren
C
open paren the fraction with numerator square root of 3 and denominator 3 comma pi over 3 close paren
D
open paren pi over 3 comma the fraction with numerator square root of 3 and denominator 3 close paren
12

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

A
pi over 2 , 330 degrees , 5 pi over 3 , 7 pi over 6 ' 2 pi over 3
B
pi over 2 , 2 pi over 3 , 7 pi over 6 , 5 pi over 3 , 330 degrees
C
330 degrees , 5 pi over 3 , 7 pi over 6 , 2 pi over 3 , pi over 2
D
5 pi over 3 , 7 pi over 6 , 2 pi over 3 , pi over 2 , 330 degrees
14

Which of the following is the equation of the function shown in the graph?

A
y is equal to 2 cosecant open bracket 2 times open paren x plus pi close paren close bracket minus 2
B
y is equal to 0 point 5 cosecant open bracket 2 times open paren x plus pi close paren close bracket minus 4
C
y is equal to 0 point 5 secant open bracket 2 times open paren x plus pi close paren close bracket minus 4
D
y is equal to 2 secant open bracket 2 times open paren x plus pi close paren close bracket minus 2
15

On a unit circle, the vertical distance from the x -axis to a point on the perimeter of the circle is twice the horizontal distance from the y -axis to the same point. What is sine theta ?

A
the fraction with numerator square root of 5 and denominator 5
B
1 fifth
C
2
D
the fraction with numerator 2 square root of 5 and denominator 5
16

If a vertical line is dropped from the x -axis to the point open paren 12 comma negative 9 close paren in the diagram, what is the value of secant theta ?

A
5 fourths
B
negative 5 fourths
C
negative 5 thirds
D
5 thirds

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