Answered: Find all solutions of the following…

Math

Trigonometry

Find all solutions of the following trigonometric equations. (a) 4 cos? 0 - 4 cos e +1 = 0

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.3: Solving Trigonometric Equations

Problem 6ECP

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Please explain each step

3. Find all solutions of the following trigonometric equations.
(a)
4 cos? e – 4 cos 0 +1 = 0
(b)
3 tan 0 = tan 0

Expert Solution

Step 1

$P a r t a G i v e n, 4 \cos^{2} (θ) - 4 \cos (θ) + 1 = 0$

Step 2

$N o w, 4 \cos^{2} (θ) - 4 \cos (θ) + 1 = 0 \Rightarrow {(2 \cos (θ))}^{2} - 2 (2 \cos (θ)) + 1^{2} = 0 \Rightarrow {(2 \cos (θ) - 1)}^{2} = 0 \Rightarrow 2 \cos (θ) - 1 = 0 \Rightarrow \cos (θ) = \frac{1}{2} \Rightarrow θ = \frac{π}{3} + 2 πn, \frac{5 π}{3} + 2 πn ∴ θ = = \frac{π}{3} + 2 πn, \frac{5 π}{3} + 2 πn$

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