Answers PrecalculusModeling with Trigonometric Expressions and Functions: Part Two

Modeling with Trigonometric Expressions and Functions: Part Two — Test Answers

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What is the inverse of the trigonometric function in the graph?

y is equal to sine x

y is equal to arccos x

y is equal to cosine x

y is equal to arcsin x

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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

Which of the following functions is represented by the graph?

y is equal to cotangent of x minus 2

y is equal to cotangent of x plus 2

y is equal to tangent of x minus 2

y is equal to tangent of x plus 2

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

y is equal to negative 3 sine open paren x plus pi close paren plus 2

y is equal to 3 sine open paren 4 times open paren x minus pi close paren close paren plus 4

y is equal to negative 3 sine open paren 2 times open paren x plus pi close paren close paren plus 2

y is equal to 3 sine open paren 2 times open paren x plus pi close paren close paren plus 2

Which function is represented in the graph?

y is equal to inverse tangent x

y is equal to cosine x

y is equal to tangent x

y is equal to inverse cosine x

What is the equation of the given graph?

y is equal to secant of open paren x plus 2 close paren

y is equal to secant of x plus 2

y is equal to cosecant of x plus 2

y is equal to cosecant of open paren x plus 2 close paren

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 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 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 2 times open paren x minus pi close paren close paren minus 2

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

5 pi over 3 units

3 pi over 5 units

2 pi over 3 units

pi over 5 units

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 2 comma square root of 21 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 negative square root of 21 close paren

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x is equal to 0 , the water level is 19 point 5 meters (a maximum). At time x is equal to 6 point 2 6 hours, the water level is 10 point 5 meters (a minimum). The period of the function is 12 point 5 hours. After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.

12 point 5 hours

6 point 3 hours

12 point 1 hours

2 point 2 hours

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

Which of the following is the graph of y is equal to cosine of 2 x ?

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It then falls through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

Image with description A coordinate plane. The graph starts and rises to (negative 24 pi comma 1). It starts to fall through (negative 21 pi comma 0) to (negative 18 pi comma negative 1). It then rises through (negative 15 pi comma 0) to (negative 12 pi comma 1). It then falls through (negative 9 pi comma 0) to (negative 6 pi comma negative 1). It then rises through (negative 3 pi comma 0) to (0 comma 1). It then falls through (3 pi comma 0) to (6 pi comma negative 1). It then rises though (9 pi comma 0) to (12 pi comma 1). It then falls through (15 pi comma 0) to (18 pi comma negative 1). It then rises through (21 pi comma 0) to (24 pi comma 1).

Image with description A coordinate plane. The graph starts and rises to (negative 8 pi comma 1). It starts to fall through (negative 7 pi comma 0) to (negative 6 pi comma negative 1). It then rises through (negative 5 pi comma 0) to (negative 4 pi comma 1). It then falls 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 though (3 pi comma 0) to (4 pi comma 1). It then falls through (5 pi comma 0) to (6 pi comma negative 1). It then rises through (7 pi comma 0) to (8 pi comma 1).

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 though (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).

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 5 comma negative 12 close paren

open paren negative 5 comma 12 close paren

open paren negative 12 comma 5 close paren

open paren 12 comma negative 5 close paren

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 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.

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

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 pi over 6 comma 0 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 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 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 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.

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 ?

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).

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).

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).

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).

Which functions are symmetric with respect to the origin?

y is equal to arccos x and y is equal to arctan x

y is equal to arcsin x and y is equal to arccos x

y is equal to arcsin x and y is equal to arctan x

y is equal to arctan x and y is equal to operatorname ar c c o t x

Which expression is equivalent to 30 degrees ?

cosine of open paren the fraction with numerator square root of 3 and denominator 2 close paren

cosine inverse of open paren the fraction with numerator square root of 3 and denominator 2 close paren

sine of open paren the fraction with numerator square root of 3 and denominator 2 close paren

sine inverse of open paren the fraction with numerator square root of 3 and denominator 2 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 3 point 2 3 6 2 ; tangent theta almost equal to 0 point 0 9 5 5

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

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

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Modeling with Trigonometric Expressions and Functions: Part Two — Test Answers

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