Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 5.5, Problem 103E

To determine

To prove:The trigonometric expression $cos22α−sin22α=cos4α$ and check result with the help of graphing utility.

Expert Solution & Answer

Explanation of Solution

Given information:

The given trigonometric expression is $cos22α−sin22α=cos4α$ .

Formula Used:

$cos2x−sin2x=cos2x$

Proof:

Consider theleft hand side of the equation and simplify it.

$cos22α−sin22α=cos2(2α)=cos4α$

From the above, it is clear thatone side of the equation can be transformed into other side of the equation.

Check result by using graphing utility.

Start the graphing calculator.

Make sure that the calculator is in the radians mode.

Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 103E , additional homework tip 1

Press $Y=$ ley and enter the data $Y1=(cos2*X))∧2−(sin2*X))∧2$ then press $ENTER$ key and enter $Y2=cos4*X)$ .

Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 103E , additional homework tip 2

To insert $π$ in window setting, click $2nd∧$ .

Adjust the window setting: press $WINDOW$ key.

$Xmin=0Xmax=2πXscl=π/4 Ymin=−3Ymax=3Yscl=1Xres=1$

Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 103E , additional homework tip 3

Press $GRAPH$ .

Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 103E , additional homework tip 4

The above graph appears to coincide, the given equation appears to be an identity.

Hence, the result is true.

Chapter 5.5, Problem 102E

Chapter 5.5, Problem 104E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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To prove: The trigonometric expression cos 2 2 α − sin 2 2 α = cos 4 α and check result with the help of graphing utility.

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Chapter 5 Solutions