   Chapter 5, Problem 4GP Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224

Solutions

Chapter
Section Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224
Textbook Problem

Write y = sin x + cos x in the form y = A sin ( B x + C ) . First identify the values of a, b, and B. Then solve for A and C using the results from Question 3. How does this equation compare with the one you found in Question 1?

To determine

To evaluate:

The values of a, b and B then solve for A andC.

Explanation

Given information:

The equation is given as, sinx+cosx=Asin(Bx+C).

Calculation:

The equation is given as,

sinx+cosx=Asin(Bx+C).

Compare sinx+cosx with asinBx+bcosBx.

Then a=1,b=1 and B=1.

since

a=AcosC.......(1)

b=AsinC.......(2) .

Substitute 1 for a in equation 1 and equation 2 and divide bothe the equation.

11=AcosCAsinCcotC=1C=cot11C=π4,3π4

Substitute π4 for C and 1 for a in equation 1

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