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Trigonometric Functions — Test Answers

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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.

56 point 5 in.

42 point 3 in.

14 point 1 in.

22 point 5 in.

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What are the values of m and theta in the given diagram?

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

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

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

m is equal to the fraction with numerator square root of 3 and denominator 3 , theta is equal to pi over 3

Which of the following could be the equation of the function?

y is equal to 0 point 5 cosine open paren 2 times open paren x minus pi close paren close paren minus 2

y is equal to 0 point 5 cosine open paren 2 times open paren x minus pi over 2 close paren close paren plus 2

y is equal to 0 point 5 cosine open paren 4 times open paren x plus pi over 2 close paren close paren minus 2

y is equal to 0 point 5 cosine open paren 4 times open paren x plus pi close paren close paren plus 2

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

y is equal to 2 cosecant open bracket 0 point 5 times open paren x plus pi over 2 close paren close bracket minus 1

y is equal to 2 cosecant open bracket 2 times open paren x plus pi over 4 close paren close bracket minus 1

y is equal to 0 point 5 cosecant open bracket 0 point 5 times open paren x plus pi over 2 close paren close bracket minus 1

y is equal to 0 point 5 cosecant open bracket 2 times open paren x plus pi over 4 close paren close bracket minus 1

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

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

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 7 is less than or equal to y comma y is less than or equal to 7

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 12 comma negative 5 close paren

open paren 5 comma negative 12 close paren

open paren negative 12 comma 5 close paren

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

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

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

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

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

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.

5 point 0 radians

2 point 7 radians

0 point 4 radian

1 point 0 radian

Which transformation should be applied to the graph of the function y is equal to cotangent of x to obtain the graph of the function y is equal to 6 cotangent open paren 3 x minus pi over 2 close paren plus 4 ?

a vertical stretch, a horizontal compression to make the period 2 pi over 3 , a horizontal shift of pi over 6 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period 2 pi over 3 , a horizontal shift of pi over 2 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period pi over 3 , a horizontal shift of pi over 2 units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period pi over 3 , a horizontal shift of pi over 6 units to the right, and a vertical shift of 4 units up

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 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

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

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 30

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 30

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

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

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

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 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

If cosecant theta is equal to 8 sevenths , which equation represents cotangent theta ?

cotangent theta is equal to the fraction with numerator 8 square root of 15 and denominator 15

cotangent theta is equal to the fraction with numerator square root of 15 and denominator 8

cotangent theta is equal to the fraction with numerator 7 square root of 15 and denominator 15

cotangent theta is equal to the fraction with numerator square root of 15 and denominator 7

How does the graph of y is equal to secant of open paren x plus 3 close paren minus 7 compare with the graph of y is equal to secant of x ?

It is the graph of y is equal to secant of x shifted 3 units left and 7 units up.

It is the graph of y is equal to secant of x shifted 3 units right and 7 units down.

It is the graph of y is equal to secant of x shifted 3 units left and 7 units down.

It is the graph of y is equal to secant of x shifted 3 units right and 7 units up.

Suppose you want to transform the graph of the function y is equal to tangent of open paren x plus pi over 4 close paren into the graph of the function y is equal to negative tangent times open paren x plus pi over 2 close paren Which transformations should you perform?

Reflect the graph of the first function across the x -axis, translate it pi over 4 units to the right, and translate it 2 units up.

Reflect the graph of the first function across the x -axis, translate it pi over 4 units to the left, and translate it 2 units up.

Reflect the graph of the first function across the line y is equal to negative 1 , translate it pi over 4 units to the left, and translate it 2 units up.

Reflect the graph of the first function across the line y is equal to negative 1 , translate it pi over 4 units to the right, and translate it 2 units 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 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).

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 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).

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 negative 10 sine pi t plus 35

h is equal to 10 sine pi t plus 35

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

Which is an x -intercept of the graph of the function y is equal to tangent of open paren x minus 5 pi over 6 close paren ?

open paren negative 2 pi over 3 comma 0 close paren

open paren negative pi over 3 comma 0 close paren

open paren pi over 6 comma 0 close paren

open paren 5 pi over 6 comma 0 close paren

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 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, other pairs of trigonometric ratios will have the same sum, 1 , which can then be used to find all other values.

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 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.

What is the equation of the graph?

y is equal to cosine of open paren x plus 45 degrees close paren

y is equal to sine of open paren x plus 90 degrees close paren

y is equal to cosine of open paren x plus 90 degrees close paren

y is equal to sine of open paren x plus 45 degrees close paren

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Trigonometric Functions — Test Answers

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