# The value of x to satisfy the following equation: | tan 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 32E
To determine

## To calculate: The value of x to satisfy the following equation:   |tanx|=1

Expert Solution

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

### Explanation of Solution

Given information:

|tanx|=1[0,2π]

Calculation:

Know that:

|tanx|=1|sinxcosx|=1

Now, consider the values of x in the given interval [0,2π] that cause sine and cosine value is equal to 1 . It occurs at ±12

Know that:

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

Now, the angle corresponding to the x,y co-ordinates means (12,12),(12,12),(12,12),(12,12) , a unit circle is drawn as:

Fig. Unit circle of |sinxcosx|=1

From the diagram:

|sinxcosx|=1 when the angle is π4,3π4,5π4,7π4 .

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

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