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Q5.

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Algebra 2

Found in: Page 774

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

State the amplitude, period and phase shift of the function $y = \tan (θ + 60 °)$ and then graph the function

The amplitude of $y = \tan (θ + 60 °)$ is not defined.

The period of $y = \tan (θ + 60 °)$ is $π$ .

The phase shift of $y = \tan (θ + 60 °)$ is $180 {}^{\circ}{or} π$ .

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 $y = \tan (θ + 60 °)$ .

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. Evaluating vertical shift, amplitude, period and phase shift of the given function.

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

The amplitude of $y = \tan (θ + 60 °)$ is not defined.

The period of $y = \tan (θ + 60 °)$ is $\frac{π}{|1|} = π$ .

The phase shift of $y = \tan (θ + 60 °)$ is $- 60 °$ .

Step 4. Sketch the graph of the function.

The graph of the function $y = \tan (θ + 60 °)$ is shown below.

Step 5. Conclusion.

The amplitude of $y = \tan (θ + 60 °)$ is not defined.

The period of $y = \tan (θ + 60 °)$ is $π$ .

The phase shift of $y = \tan (θ + 60 °)$ is $- 60 °$ .

Most popular questions for Math Textbooks

For Exercises $39 - 41$ , use the following information.

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What is the height of the buoy after 12 seconds?

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