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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224
Textbook Problem

Find all solutions in the interval 0 ° θ 360 ° . If rounding is necessary, round to the nearest tenth of a degree.

4 cos 2 θ + 2 sin θ = 1

3
To determine

To calculate:

All the solutions of the given trigonometric equation.

Explanation

Given information:

4cos2θ+2sinθ=1

Concept Used:

To find the solution of the equation we factorise the equation by taking out common terms.

Also use identity cos2θ=12sin2θ to write each term in same trigonometric function

Calculation:

The given equation is:

4cos2θ+2sinθ=1

Using cos2θ=12sin2θ

4(12sin2θ)+2sinθ=148sin2θ+2sinθ1=0

On simplifying we get

8sin2θ2sinθ3=0

Now factorise the equation

8sin2θ(64)sinθ3=08sin2θ6sinθ+4sinθ3=02sinθ

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