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Chapter 8: Q. 44 (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 0,2蟺

h(x)=cos(2x)cos(x)

Short Answer

Expert verified

(a) h(x)=12cos(3x)+cosx

(b)

Step by step solution

01

Step 1. Given Information

The given function ish(x)=cos(2x)cosx

02

Part(a) Step 1. Calculation 

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

h(x)=12(cos(2x+x)+cos(2x-x))=12cos(3x)+cosx

03

Part(b) Step 1. Explanation and Graph 

Graph the component functions obtained in the above part in the 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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