What is the general solution for 3=6sin(θ) ?

The general solution for 3=6sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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3=6sin(θ)

3 = 6 sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

3 = 6 sin (θ)

Switch sides

6 sin (θ) = 3

Divide both sides by

6

6 sin (θ) = 3

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{3}{6}

Simplify

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

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 = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (a) = \frac{1}{4}

33 sec (θ) + 4 = - 2

- sin (\frac{x}{2}) + sin (x) = 0

3 sin (2 θ) = 2 cos (2 θ)

cos (x) + cos^{2} (x) = 0

What is the general solution for 3=6sin(θ) ?
The general solution for 3=6sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin