# The value of x to satisfy the following equation: 2 sin 2 x = 1

### 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 30E
To determine

## To calculate: The value of x to satisfy the following equation:   2sin2x=1

Expert Solution

The values of x for the interval [0,2π] to satisfy eq. 2sin2x=1 are π4,3π4,5π4,7π4 .

### Explanation of Solution

Given information:

2sin2x=1[0,2π]

Calculation:

Know that:

2sin2x=1sin2x=12sinx=±12

Now, consider the values of x in the given interval [0,2π] that cause sine value is equal to ±12 .

Know that:

The circle has co-ordinates (x,y)=(cosθ,sinθ) with the radius 1 .

Now, the angle corresponding to the y co-ordinates means sinx=±12 , a unit circle is drawn as:

Fig. Unit circle of sinx=±12

From the diagram:

Sine is equal to ±12 when the angle is π4,3π4,5π4,7π4 .

Therefore, the values of x for the interval [0,2π] to satisfy eq. 2sin2x=1 are π4,3π4,5π4,7π4 .

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