   Chapter 8.2, Problem 62E ### 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. tan 2 θ = 3

To determine

The values of θ for the trigonometric equation tan2θ=3 and verify the result by graphing utility tool.

Explanation

Given Information:

The provided trigonometric equation is, tan2θ=3.

Consider the trigonometric equation, tan2θ=3

Simplify the provided trigonometry equation,

tan2θ=3tanθ=±3

Since, tangent is positive in first and third quadrants, while tangent is negative in second and fourth quadrants.

Thus, there are four solutions for trigonometric equation tan2θ=3 for 0θ2π, which can be mathematically determined as:

tanθ=3tanθ=tanπ3θ=π3=1.047197551,

tanθ=3tanθ=tan4π3θ=4π3=4.188790205

tanθ=3tanθ=tan2π3θ=2π3=2.094395102

tanθ=3tanθ=tan5π3θ=5π3=5.235987756

Therefore, the values of θ for the trigonometric equation tan2θ=3 are θ=π3, θ=2π3, θ=4π3 and θ=5π3.

To verify the result use Ti-84 calculator,

Rewrite the provided trigonometric equation, tan2θ=3 as,

tan2θ=3tanθ=±3

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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