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

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

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3sin(θ)=3

3 sin (θ) = 3

θ = \frac{π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

3 sin (θ) = 3

Divide both sides by

3

3 sin (θ) = 3

Divide both sides by

3

\frac{3 sin ( θ )}{3} = \frac{3}{3}

Simplify

sin (θ) = 1

sin (θ) = 1

General solutions for

sin (θ) = 1

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}{2} + 2 πn

θ = \frac{π}{2} + 2 πn

cos (2 θ) + sin (θ) = 0, 0 \leq θ < 2 π

cos (\frac{π}{3} x - \frac{π}{4}) = \frac{2}{2}

\frac{sin ( x )}{1} = \frac{3}{5}

x, e^{y} = tan (x + \frac{π}{3})

cos (x) = (sin (x))^{2} - 1

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