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Chapter 8: Q. 41 (page 550)

(a) Use the Product-to-Sum Formulas to express each product as a sum, and

(b) Use the method of adding y-coordinates to graph each function on the interval 0,2π

f(x)=sin(2x)sinx

Short Answer

Expert verified

(a)f(x)=12cosx-cos(3x)

(b)

Step by step solution

01

Step 1. Given Information

The given function isf(x)=sin2xsinx

02

Part(a) Step 1. Calculation

First multiply and divide the given function by 2 and then use the product formula to obtained the required result.

f(x)=12(2sin(2x)sinx)=12(cos(2x-x)-cos(2x+x))=12cosx-cos(3x)

03

Part(b) Step 1. Explanation and Graph

Graph the component functions obtained in above part in same coordinate system and then select several values of x at which we can compute the value of y.

Plot the points and connect them to get the required graph.

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