   Chapter 8.2, Problem 31E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating Trigonometric Functions In Exercises 19-32, evaluate the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3. 10 π 3

To determine

To calculate: The value of six trigonometric functions of an angle 10π3 without using a calculator.

Explanation

Given Information:

The angle is 10π3.

Formula used:

Trigonometric values of Common angles:

 θ(degrees) 0° 30° 45° 60° 90° 180° 270° θ(radians) 0 π6 π4 π3 π2 π 3π2 sinθ 0 12 22 32 1 0 −1 cosθ 1 32 22 12 0 −1 0 tanθ 0 33 1 3 Undefined 0 Undefined

Calculation:

Consider the angle θ=10π3, it lies in third quadrant.

First find the reference angle of θ=10π3.

reference angle of 10π3=10π33π=10π9π3=π3

Since, the Tangent and Cotangent are positive and remaining trigonometric functions are negative in the III quadrant.

So, we can write the six trigonometric functions as,

sin(10π3)=sin(π3)cos(10π3)=cos(π3)tan(10π3)=tan(π3)csc(10π3)=csc(π3)

Remaining trigonometric functions as,

sec(10π3)=sec(π3)cot(10π3)=cot(π3)

Now, evaluate the value of six trigonometric functions for reference angle θ=π3 using Trigonometric values of common angles

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