Chapter 6.3, Problem 34E

### Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759

Chapter
Section

### Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759
Textbook Problem

# Values of Trigonometric Functions Find the exact value of the trigonometric function.34. cos 7 π 4

To determine

To find: The value of trigonometric function.

Explanation

Given:

The given trigonometric function is cos(7π4) .

Definition:

The reference angle θ¯ is the smallest angle formed by the terminal side of θ and the x-axis.

Calculation:

The acute angle formed by the terminal side of angle 7π4 and x-axis is the reference angle θ¯ .

Figure (1)

Figure (1) shows the reference angle of 7π4 .

Since, the terminal side of given angle lies in quadrant (IV) in which cosine is positive, the reference angle is,

θ¯=2π7π4=8π7π4=π4

The value of cosine is,

cos(7π4)=cos(π4)

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