   Chapter 8.2, Problem 30E ### 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
1 views

# Evaluating Trigonometric Functions In Exercises 19-32, evaluate the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3. 510 °

To determine

To calculate: The value of six trigonometric functions of an angle 510° without using a calculator.

Explanation

Given Information:

The angle is 510°.

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=510°

First, find the reference angle of θ=510°.

reference angle of 510°=3(180°)510°=540°510°=30°

Since, the Sine and Cosecant are positive and remaining trigonometric functions are negative in the II quadrant.

So, we can write the six trigonometric functions as,

sin(510°)=sin(30°)cos(510°)=cos(30°)tan(510°)=tan(30°)csc(510°)=csc(30°)

Remaining trigonometric functions as,

sec(510°)=sec(30°)cot(510°)=cot(30°)

Now, evaluate the value of six trigonometric functions for reference angle θ=30° using Trigonometric values of common angles.

sin(30°)=12cos(30°)=32tan(30°)=33

Evaluate the csc(30°) using reciprocal identities

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