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Trigonometric Functions — Test Answers

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What is 270 degrees converted to radians?

pi over 6

3 pi over 2

3 halves

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

2 pi , 38 degrees , 80 degrees , pi over 4 , 7 pi over 6

38 degrees , pi over 4 , 80 degrees , 7 pi over 6 , 2 pi

38 degrees , 80 degrees , pi over 4 , 7 pi over 6 , 2 pi

2 pi , 7 pi over 6 , 80 degrees , pi over 4 , 38 degrees

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.

1 point 0 radian

2 point 7 radians

5 point 0 radians

0 point 4 radian

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 ?

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

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

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

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

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

all real numbers negative 7 is less than or equal to y comma y is less than or equal to 7

all real numbers negative 1 is less than or equal to y comma y is less than or equal to 1

all real numbers negative 5 is less than or equal to y comma y is less than or equal to 3

all real numbers negative 7 is less than or equal to y comma y is less than or equal to negative 1

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 3 sine open paren pi over 2 times open paren t plus 2 close paren close paren plus 5 Which of the following is the graph of this equation?

Image with description A first-quadrant coordinate plane. The horizontal axis goes from 0 to 8 and is labeled Time, in seconds. The vertical axis goes from 0 to 20 and is labeled Height, in inches. Points start at (0 comma 10) and rise to (2 comma 16). The points fall to (6 comma 4), and rise back to (9 comma 16).

Image with description A first-quadrant coordinate plane. The horizontal axis goes from 0 to 10 and is labeled Time. The vertical axis goes from 0 to 10 and is labeled Height. Points start at (0 comma 5 point 5) and rise to (1 comma 8). The points fall to (3 comma 2), and rise to (5 comma 8). The points fall to (7 comma 2), and rise to (9 comma 8). Then the points go down.

Image with description A first-quadrant coordinate plane. The horizontal axis goes from 0 to 10 and is labeled Time. The vertical axis goes from 0 to 10 and is labeled Height. Points start at (0 comma 8) and fall to (4 comma 2). The points rise to (8 comma 8), and rise back to (10 comma 4).

Image with description A first-quadrant coordinate plane. The horizontal axis goes from 0 to 10 and is labeled Time, in seconds. The vertical axis goes from 0 to 10 and is labeled Height, in inches. Points start at (0 comma 4 point 5) and fall to (1 comma 2). The points rise to (3 comma 8), and rise back to (5 comma 2). The points rise to (7 comma 8), and fall to (9 comma 2). Then the points go up.

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

Image with description A coordinate plane. The graph starts and rises to (0 comma negative 2). It starts to fall through (pi over 2 comma negative 3) to (pi comma negative 4). It then rises through (3 pi over 2 comma negative 3) to (2 pi comma negative 2).

Image with description A coordinate plane. The graph starts and rises to (0 comma 3). It starts to fall through (pi over 2 comma 0) to (pi comma negative 3). It then rises through (3 pi over 2 comma 0) to (2 pi comma 3).

Image with description A coordinate plane. The graph starts and rises to (0 comma 4). It starts to fall through (pi over 2 comma 3) to (pi comma 2). It then rises through (3 pi over 2 comma 3) to (2 pi comma 4).

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).

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

f of x is equal to negative sine times x minus 1

f of x is equal to negative 2 cosine x minus 1

f of x is equal to negative cosine times x

f of x is equal to negative 2 sine x minus 1

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

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

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

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

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

The height, h , in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t , in hours? Assume that the time at t is equal to 0 is 12:00 a.m.

h is equal to cosine of open paren pi over 6 t close paren plus 9

h is equal to cosine of open paren pi over 12 t close paren plus 9

h is equal to 0 point 5 cosine open paren pi over 6 t close paren plus 9 point 5

h is equal to 0 point 5 cosine open paren pi over 12 t close paren plus 9 point 5

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?

r is equal to 14 sixths

r is equal to 6 times 14

r is equal to 6 plus 14

r is equal to 6 over 14

Three trigonometric functions for a given angle are shown. cosecant theta is equal to 13 over 12 , secant theta is equal to negative 13 fifths , cotangent theta is equal to negative 5 over 12 What are the coordinates of point open paren x comma y close paren on the terminal ray of angle theta , assuming that the values above were not simplified?

open paren negative 5 comma 12 close paren

open paren 5 comma negative 12 close paren

open paren 12 comma negative 5 close paren

open paren negative 12 comma 5 close paren

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.

h is equal to negative 10 sine open paren pi over 15 t close paren plus 35

h is equal to 10 sine open paren pi over 15 t close paren plus 35

h is equal to 10 sine pi t plus 35

h is equal to negative 10 sine pi t plus 35

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 ?

cap p times open paren negative square root of 21 comma negative 2 close paren

cap p times open paren square root of 21 comma negative 2 close paren

cap p times open paren negative 2 comma square root of 21 close paren

cap p times open paren negative 2 comma negative square root of 21 close paren

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 ?

sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 3 point 0 7 8 0

sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 0 point 3 2 4 9

sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 0 point 0 9 5 5

sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 10 point 4 7 3 1

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.

y is equal to 30 sine open paren pi over 15 t close paren plus 10

y is equal to 10 sine open paren pi over 15 t close paren plus 10

y is equal to 10 sine open paren pi over 15 t close paren plus 30

y is equal to 30 sine open paren pi over 15 t close paren plus 30

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?

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.

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.

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.

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.

What is the approximate length of arc s on the circle? Use 3 point 1 4 for pi Round your answer to the nearest tenth.

14 point 1 in.

22 point 5 in.

56 point 5 in.

42 point 3 in.

The height, h , in feet of a buoy in relation to sea level as a function of time, t , in seconds can be modeled by the given graph. How long does it take for the buoy to go from its highest point to its lowest point and then back to its highest point?

1 second

3 seconds

2 seconds

4 seconds

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

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.

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.

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.

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.

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Trigonometric Functions — Test Answers

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