   Chapter 8.2, Problem 68E ### 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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# Solving a Trigonometric Equation In Exercises 61-70, solve the equation for θ . Assume 0 ≤ θ ≤ 2 π . For some of the equations, you should use the trigonometric identities listed in this section. Use a spreadsheet or a graphing utility to verify your results. See Example 7. sec θ csc θ = 2 csc θ

To determine

To calculate: The values of θ for the trigonometric equation secθcscθ=2cscθ and verify the result by graphing utility tool.

Explanation

Given Information:

The provided trigonometric equation is,

secθcscθ=2cscθ

Calculation:

Consider the trigonometric equation, secθcscθ=2cscθ.

Simplify the provided trigonometry equation,

secθcscθ2cscθ=0cscθ(secθ2)=0

Further solve,

secθ2=0secθ=2

Or,

cscθ=0

The equation cscθ=0 doesn’t have any solution. As cosec don’t have zero value for any θ.

Since, sec is negative in third and fourth quadrants, Thus, there are two solutions for trigonometric equation secθcscθ=2cscθ in the interval 0θ2π, which is as follows:

First value:

θ=π3=1.04179

Second value:

θ=5π3=5.23598

To verify the result use Ti-84 calculator,

Rewrite the provided trigonometric equation, secθcscθ=2cscθ as,

secθcscθ=2cscθ(1cosθ)(1sin)=2sinθ2cosθ=1

The steps used to find the solution of the trigonometric function within range of 0θ2π using graphic calculator Ti-84, which is given as below:

Step 1: Press ON button and then press Y= button

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