   Chapter 8.2, Problem 69E ### 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. cos 2 θ + sin θ = 1

To determine

To calculate: The values of θ for the trigonometric equation cos2θ+sinθ=1.

Explanation

Given Information:

The provided trigonometric equation is,

cos2θ+sinθ=1

Formula used:

The formula for the trigonometrical identity is:

cos2θ=1sin2θ

Calculation:

Consider the trigonometric equation:

cos2θ+sinθ=1

Simplify as:

1sin2θ+sinθ=1sin2θ+sinθ=0sinθ(sinθ1)=0

So,

sinθ=0θ=0,π,2π

Or,

sinθ1=0

θ=π2

Check:

Consider the provided trigonometric equation.

cos2θ+sinθ=1cos2θ+sinθ1=0

Consider the trigonometric equation:

Y=cos2θ+sinθ1

The steps used to find the solution of the trigonometric function Y=cos2θ+sinθ1 within range of 0θ2π using graphic calculator Ti-84, which can be given as below:

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

Step 2: Then, enter the function Y=cos2θ+sinθ1 as Y=cos2X+sinX1.

Step 3: Now, press window button and set the window as Xmin=0.50, Xmax=6.50, Xscl=2, Ymin=1, Ymax=1, and Yscl=0

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