   Chapter 8.2, Problem 63E ### 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

# 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. tan 2 θ − tan θ = 0

To determine

The values of θ for the trigonometric equation tan2θtanθ=0 and verify the result by graphing utility tool.

Explanation

Given Information:

The provided trigonometric equation is, tan2θtanθ=0.

Consider the trigonometric equation, tan2θtanθ=0.

Simplify the provided trigonometry equation,

tan2θtanθ=0tanθ(tanθ1)=0

Further solve,

tanθ=0

And,

tanθ1=0tanθ=1

Since, tanθ is zero at θ=0, θ=π and θ=2π, while tangent is positive in first and third quadrants,

Thus, there are five solutions for trigonometric equation tan2θtanθ=0 for 0θ2π, which can be mathematically determined as:

First value:

tanθ=0tanθ=tan0θ=0,

Second value:

tanθ=0tanθ=tanπθ=π=3.141592654

Third value:

tanθ=0tanθ=tan2πθ=2π=6.283185307

Fourth value:

tanθ=1tanθ=tanπ4θ=π4=0.785398163

Fifth value:

tanθ=1tanθ=tan5π4θ=5π4=3.926990817

Therefore, the values of θ for the trigonometric equation tan2θtanθ=0 are θ=0, θ=π4 θ=π, θ=5π4 and θ=2π

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 