What is the general solution for 0=3sin(θ) ?

The general solution for 0=3sin(θ) is θ=2pin,θ=pi+2pin

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0=3sin(θ)

0 = 3 sin (θ)

θ = 2 πn, θ = π + 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = 3 sin (θ)

Switch sides

3 sin (θ) = 0

Divide both sides by

3

3 sin (θ) = 0

Divide both sides by

3

\frac{3 sin ( θ )}{3} = \frac{0}{3}

Simplify

sin (θ) = 0

sin (θ) = 0

General solutions for

sin (θ) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

2 cos^{(2)} (x) + 32 sin (x) = 4

3 cos (θ) + 2 sec (θ) + 7 = 0

2 cos^{2} (x) + sin (x) - 1 = 0, (0, 2 π)

4 cos^{2} (x) - 2 cos (x) - 1 = 0

cos^{2} (x) - 4 cos (x) - 5 = 0

What is the general solution for 0=3sin(θ) ?
The general solution for 0=3sin(θ) is θ=2pin,θ=pi+2pin