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Chapter 8: Q. 46 (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]

g(x)=2sinxcos(3x)

Short Answer

Expert verified

(a) g(x)=sin(4x)-sin(2x)

(b)

Step by step solution

01

Step 1. Given Information 

The given function isg(x)=2sinxcos(3x)

02

Part(a) Step 1. Calculation  

Use the product to sum formula to obtain the required result.

g(x)=sin(3x+x)-sin(3x-x)=sin(4x)-sin(2x)

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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