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(35 POINTS!!) Based on the graph of the trigonometric functions f (θ) = 4sin θ + 1 and g (θ) = cos 2θ, at
what value(s) on the interval [0, 2π) does f (θ) = g (θ)?

A. 0, π
B. pi over 2 comma 5 times pi over 2
C. 5 times pi over 4 comma 7 times pi over 4
D. pi over 4 comma 3 times pi over 4 comma 5 times pi over 4 comma 7 times pi over 4

Respuesta :

The values on the interval [0, 2π) that makes f (θ) equal to g(θ) is; A: 0, π

How to solve Trigonometric Functions?

We are given the trigonometric functions;

f(θ) = 4sin θ + 1

g(θ) = cos 2θ

We know from trigonometric identities that;

cos 2θ = 1 - 2sin²θ

At f(θ) = g(θ), we have;

4sin θ + 1 = 1 - 2sin²θ

2sin²θ + 4sin θ = 0

2sinθ(sin θ + 2) = 0

2sinθ = 0

θ = sin⁻¹(0/2)

θ = 0, π

Read more about Trigonometric Functions at; https://brainly.com/question/6904750

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