   Chapter 8.2, Problem 65E ### 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. sin 2 θ − cos θ = 0

To determine

To calculate: The values of θ for the trigonometric equation sin2θcosθ=0 and verify the result by graphing utility tool.

Explanation

Given Information:

The provided trigonometric equation is, sin2θcosθ=0.

Formula used:

Double angle formula for trigonometric identity,

sin2θ=2sinθcosθ

Calculation:

Consider the trigonometric equation, sin2θcosθ=0.

Simplify the provided trigonometry equation,

2sinθcosθcosθ=0cosθ(2sinθ1)=0

Further solve.

cosθ=0

And,

2sinθ1=0sinθ=12

Since, cosine is zero at θ=π2, θ=3π2, while Sine is positive in first and second quadrants,

Thus, there are four solutions for trigonometric equation sin2θcosθ=0 for 0θ2π, which can be mathematically determined as:

First value:

cosθ=0cosθ=cosπ2θ=π2=1.570796327

Second value:

cosθ=0cosθ=cos3π2θ=4.71238898

Third value:

sinθ=12sinθ=cosπ6θ=π6=0.523598775

Fourth value:

sinθ=12sinθ=cos5π6θ=5π6=2.617993878

To verify the result use Ti-84 calculator,

Rewrite the provided trigonometric equation, sin2θcosθ=0 as,

2sinθcosθcosθ=0cosθ(2sinθ1)=0

Further solve

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