# The value of x to satisfy the following equation: sin 2 x = cos x ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter C, Problem 31E
To determine

## To calculate: The value of x to satisfy the following equation:   sin2x=cosx

Expert Solution

The values of x for the interval [0,2π] to satisfy eq. sin2x=cosx are π6,π2,5π63π2 .

### Explanation of Solution

Given information:

sin2x=cosx[0,2π]

Formula Used:

The double angle theorem:

sin2x=2sinxcosx

Calculation:

Know that:

sin2x=cosx2sinxcosx=cosx2sinxcosxcosx=0cosx(2sinx1)=0

Here are two cases:

Case 1: cosx=0

This case occurs at odd multiple of π2 . So values of x are π2,3π2 for the interval [0,2π] .

Case 1: 2sinx1=0

Solve this equation:

2sinx1=0sinx=12

So, the values of x in the given interval [0,2π] that cause sine value is equal to 12 are π6 are 5π6 .

Therefore, the values of x for the interval [0,2π] to satisfy eq. sin2x=cosx are π6,π2,5π63π2 .

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