   Chapter 8.2, Problem 19E ### 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, evaluation the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3.60°

To determine

To calculate: The values of six trigonometric functions of the angle 60° without a calculator.

Explanation

Given Information:

The provided angle is 60°.

Formula used:

The trigonometric values of some common angles are provided in the table.

 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

The reciprocal identities for trigonometric functions are,

cscθ=1sinθ,secθ=1cosθ and cotθ=1tanθ

Calculation:

Consider the angle, θ=60°

Now, evaluate the values of six trigonometric functions for θ=60° by the use of trigonometric values of common angles.

sin60°=32cos60°=12tan60°=3

Evaluate the csc60° by reciprocal identity cscθ=1sinθ

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