Find &#x03B8;<!-- θ --> from the equation cos &#x2061;<!-- ⁡ --> &#x03B8;<!-- θ -->

oleifere45

oleifere45

Answered question

2022-06-06

Find θ from the equation cos θ cos 2 θ cos 3 θ = 1 / 4

Answer & Explanation

Sage Mcdowell

Sage Mcdowell

Beginner2022-06-07Added 19 answers

We have,
cos θ cos 2 θ cos 3 θ = 1 4
4 cos θ cos 2 θ cos 3 θ = 1
( 2 cos 3 θ cos θ ) 2 cos 2 θ = 1
( cos 4 θ + cos 2 θ ) 2 cos 2 θ 1 = 0
2 cos 2 θ cos 4 θ + cos 4 θ = 0
This gives us,
cos 4 θ = 0 cos 2 θ = 1 2
where ∣ stands for "or". I hope you will be able to take it from here.

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