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Q27.

Expert-verified

Algebra 2

Found in: Page 775

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

State the vertical shift, equation of midline, amplitude and period of the function $y = \cos (θ) - 5$ and then graph the function.

The vertical shift of $y = \cos (θ) - 5$ is $- 5$ .

The equation of midline of $y = \cos (θ) - 5$ is $y = - 5$ .

The amplitude of $y = \cos (θ) - 5$ is 1.

The period of $y = \cos (θ) - 5$ is $2 π$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given function is $y = \cos (θ) - 5$ .

Step 2. Concept used.

A function of the form:

$y = a \sin b (θ - h) + k, y = a \cos b (θ - h) + k and y = a \tan b (θ - h) + k$ has vertical shift $(k)$ . And, a period of $\frac{360 °}{|b|} or \frac{2 π}{|b|}$ for sine, cosecant, secant and cosine functions and a period of $\frac{180 °}{|b|} or \frac{π}{|b|}$ for tangent and cotangent function. The phase shift for the functions is $(h)$ .

The amplitude of secant, cosecant, tangent and cotangent functions is not defined.

The equation for the midline is written as, $y = k$ . A midline is a new reference line when the parent graph is stretched vertically up or down and then the graph oscillates about new reference line called the midline.

Step 3. Calculation.

With the help of concept stated above, the vertical shift, equation of midline, amplitude and period of the function is evaluated as:

The vertical shift of $y = \cos (θ) - 5$ is $- 5$ .

The equation of midline of $y = \cos (θ) - 5$ is $y = - 5$ .

The amplitude of $y = \cos (θ) - 5$ is $|1| = 1$ .

The period of $y = \cos (θ) - 5$ is $\frac{2 π}{|1|} = 2 π$ .

Step 4. Sketch the graph of the function.

The graph of the function $y = \cos (θ) - 5$ is shown below.

Step 5. Conclusion.

The vertical shift of $y = \cos (θ) - 5$ is $- 5$ .

The equation of midline of $y = \cos (θ) - 5$ is $y = - 5$ .

The amplitude of $y = \cos (θ) - 5$ is $|1| = 1$ .

The period of $y = \cos (θ) - 5$ is $\frac{2 π}{|1|} = 2 π$ .

Most popular questions for Math Textbooks

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