Trigonometric equation; finding all solutions I'm having a hard time with trigonometric equations. I need to find all solutions to the following equation: 4 sin^2 theta=3 Any help will be appreciated.

kaltEvallwsr

kaltEvallwsr

Answered question

2022-11-13

Trigonometric equation; finding all solutions
I'm having a hard time with trigonometric equations. I need to find all solutions to the following equation:
4 sin 2 θ = 3
Any help will be appreciated.

Answer & Explanation

Phiplyrhypelw0

Phiplyrhypelw0

Beginner2022-11-14Added 24 answers

Hint: Your equation reduces to 2 cases:
sin θ = 3 2
and
sin θ = 3 2
Kale Sampson

Kale Sampson

Beginner2022-11-15Added 6 answers

Rewrite the equation as
4 sin 2 θ 2 = 1 2 cos 2 θ = 1 cos 2 θ = 1 2
so the solutions are:
2 θ ± 2 π 3 mod 2 π θ ± π 3 mod π .

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