BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter C, Problem 34E
To determine

To calculate:

The value of x to satisfy the following inequality equation:

  2cosx+1>0

Expert Solution

Answer to Problem 34E

The values of x for the interval [0,2π] to satisfy eq. sinx12 are [0xπ6] and [5π6xπ] .

Explanation of Solution

Given information:

  2cosx+1>0[0,2π]

Calculation:

Know that:

  2cosx+1>02cosx>1cosx>12

Consider;

The unit circle with co-ordinates (x,y)=(cosx,sinx) and radius 1 to find out the values of x for the interval [0,2π] that cause cosx>12 .

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 34E

Fig. Unit circle

From the unit circle figure:

The x coordinate or cosine value is positive and should greater than 12 , is observed in the first and fourth quadrant.

So, the values gets as [0xπ2] and [3π2x2π] .

Cosine value is greater than or equal to 12 in the third and second quadrant for the x value of interval [0xπ6] .

In the first quadrant cosx>12 , x value of interval [π2x2π3]

In the third quadrant cosx>12 , x value of interval [4π3x3π2]

Therefore, the values of x for the interval [0,2π] to satisfy eq. 2cosx+1>0 are [0x2π3] and [4π3x2π] .

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