What is the general solution for 0=4|sin(6θ)| ?

The general solution for 0=4|sin(6θ)| is θ=(pin)/3 ,θ= pi/6+(pin)/3

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0=4|sin(6θ)|

0 = 4 ∣ sin (6 θ) ∣

θ = \frac{πn}{3}, θ = \frac{π}{6} + \frac{πn}{3}

Solution steps

0 = 4 ∣ sin (6 θ) ∣

Switch sides

4 ∣ sin (6 θ) ∣ = 0

Divide both sides by

4

∣ sin (6 θ) ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

sin (6 θ) = 0

General solutions for

sin (6 θ) = 0

6 θ = 0 + 2 πn, 6 θ = π + 2 πn

Solve

6 θ = 0 + 2 πn : θ = \frac{πn}{3}

Solve

6 θ = π + 2 πn : θ = \frac{π}{6} + \frac{πn}{3}

θ = \frac{πn}{3}, θ = \frac{π}{6} + \frac{πn}{3}

5 sin^{2} (θ) - 11 sin (θ) + 6 = 0

cos (x) = \frac{11}{14}, sin (x)

sin^{2} (2 x) + cos^{2} (3 x) = 1

sin (θ) = 0.9848

cot^{(2)} (x) + 2 cot (x) + 1 = 0

What is the general solution for 0=4|sin(6θ)| ?
The general solution for 0=4|sin(6θ)| is θ=(pin)/3 ,θ= pi/6+(pin)/3