AnswersAlgebra IITrigonometric Functions

Practice Test Answers

18 verified answers
1
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What is the amplitude of the cosine function corresponding to the secant function graphed?

A
negative 2
B
negative 1
C
2
D
3
2
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Which formula gives the zeros of y is equal to sine of x ?

A
k pi over 2 for any integer k
B
k pi over 2 for any positive integer k
C
k pi for any positive integer k
D
k pi for any integer k
3

The height, h , in feet of a ball suspended from a spring as a function of time, t , in seconds can be modeled by the equation h is equal to A sine open paren b times open paren t minus h close paren close paren plus k What is the height of the ball at its equilibrium?

A
A feet
B
b feet
C
k feet
D
h feet
4

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 4 pi plus 8 n pi , where n is any integer
B
all real numbers except 8 pi plus 4 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 8 pi plus 8 n pi , where n is any integer
5

Which of the following is cotangent of theta secant of theta in simplified form?

A
negative 1
B
cosecant theta
C
1
D
tangent theta
6

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 3 , 5 pi over 6 , 4 pi over 3
D
pi over 2 , 5 pi over 4 , 7 pi over 4
7

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 the fraction with numerator square root of 3 and denominator 3 comma pi over 3 close paren
C
open paren square root of 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
8

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 1; the fraction with numerator open paren cosine of x over sine of x close paren and denominator sine of x
C
step 4; cosine of x
D
step 4; cosecant of x
9

A student uses the equation tangent theta is equal to the fraction with numerator s squared and denominator 49 to represent the speed, s , in feet per second, of a toy car driving around a circular track having an angle of incline theta , where sine theta is equal to 1 half To solve the problem, the student used the given value of sine theta to find the value of tangent theta and then substituted the value of tangent theta in the equation above to solve for s What is the approximate value of s , the speed of the car in feet per second?

A
9 point 2
B
5 point 3
C
28 point 3
D
7 point 5
10

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 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).
B
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).
C
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).
D
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).
11

An angle in standard position measures pi over 2 radians, and cap p times open paren 0 comma 1 close paren is on the terminal side of the angle. What is the value of the cosine of this angle?

A
negative 1
B
undefined
C
1
D
0
12

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 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 .
C
The graph of the function is the graph of f of x is equal to negative 2 sine x shifted 3 units up.
D
The amplitude of the function is 2 .
13

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

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

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
5 point 7 ft
C
7 point 0 ft
D
6 point 3 ft
15

What is the general equation of a sine function with an amplitude of 6 , a period of pi over 4 , and a horizontal shift of pi over 2 ?

A
y is equal to 6 sine open paren 8 times open paren x minus pi over 2 close paren close paren
B
y is equal to 6 sine 8 x plus pi over 2
C
y is equal to 8 sine open paren 4 times open paren x minus pi over 2 close paren close paren
D
y is equal to sine of open paren 8 times open paren x minus pi over 2 close paren close paren
16

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3 point 2 5 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8 point 7 5 meters. Which of the following equations models d , the depth of the water in meters, as a function of time, t , in hours? Let t is equal to 0 be 12:00 a.m.

A
d is equal to negative 3 point 7 5 cosine open paren 4 pi over 31 t close paren plus 5
B
d is equal to negative 3 point 7 5 cosine open paren 4 pi over 29 t close paren plus 5
C
d is equal to negative 2 point 7 5 cosine open paren 4 pi over 29 t close paren plus 6
D
d is equal to negative 2 point 7 5 cosine open paren 4 pi over 31 t close paren plus 6
17

The parent cosecant function is shifted 2 units down, and its period is changed to 6 pi Which of the following is the graph of the transformed function?

A
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (3 by 2 pi comma1) and (negative 9 by 2 pi comma 1). Another line y equals negative 1 touches at (9 by 2 pi comma negative 1) and (negative 3 by 2 pi comma negative 1).
B
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (3 by 2 pi comma negative 1) and (negative 9 by 2 pi comma negative 1). Another line y equals negative 3 touches at (3 by 2 pi comma negative 3) and (negative 9 by 2 pi comma negative 3).
C
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 3 touches at (3 pi comma negative 3) and (negative 3 pi comma negative 3).
D
Image with description On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 2 touches at (3 pi comma negative 1) and (negative 3 pi comma negative 1).
18

An angle that shares the same sine value of an angle that measures 5 pi over 4 radians is located where?

A
Quadrant I
B
along an axis
C
Quadrant IV
D
Quadrant II

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