   Chapter 8.2, Problem 7CP ### 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

# Solve the equation for θ. sin   2 θ + sin θ = 0 ,         0 ≤ θ ≤ 2 π

To determine

To calculate: The values of θ for the trigonometric equation sin2θ+sinθ=0.

Explanation

Given Information:

The provided trigonometric equation is, sin2θ+sinθ=0.

Formula used:

Double angle formula for trigonometric identity:

sin2θ=2sinθcosθ

Calculation:

Consider the trigonometric equation, sin2θ+sinθ=0

Simplify the provided trigonometry equation,

sin2θ+sinθ=02sinθcosθ+sinθ=0sinθ(2cosθ+1)=0

Further solve.

sinθ=0

And,

2cosθ+1=0cosθ=12

Since sine is zero at θ=0, θ=π and θ=2π, while cosine is negative in second and third quadrants

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