Chapter 8: Q. 42 (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 $[0, 2 π]$
role="math" localid="1646907271880" $F (x) = \sin (3 x) \sin x$

Short Answer

Expert verified

$(a) F (x) = \frac{1}{2} [\cos (2 x) - \cos (4 x)]$

(b)

Step by step solution

Step 1. Given Information

The given function is $F (x) = \sin (3 x) \sin x$

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.

$F (x) = \frac{1}{2} (\cos (3 x - x) - \cos (3 x + x)) = \frac{1}{2} (\cos (2 x) - \cos (4 x))$

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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(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 $[0, 2 π]$
role="math" localid="1646907271880" $F (x) = \sin (3 x) \sin x$

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Calculation

Part(b) Step 1. Explanation and Graph

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(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 0,2πrole="math" localid="1646907271880" F(x)=sin(3x)sinx

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Calculation

Part(b) Step 1. Explanation and Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

(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 $[0, 2 π]$
role="math" localid="1646907271880" $F (x) = \sin (3 x) \sin x$