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

The general solution for 6sin(θ)-6=0 is θ= pi/2+2pin

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6sin(θ)-6=0

6 sin (θ) - 6 = 0

θ = \frac{π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (θ) - 6 = 0

Move

6

to the right side

6 sin (θ) - 6 = 0

Add

6

to both sides

6 sin (θ) - 6 + 6 = 0 + 6

Simplify

6 sin (θ) = 6

6 sin (θ) = 6

Divide both sides by

6

6 sin (θ) = 6

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{6}{6}

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

tan (5 x) = 3

cos (2 θ) = 3 cos (θ) - 2

sin (x) = - \frac{5}{13}

9 tan^{2} (x) - 3 = 0

cos (x) = - \frac{2}{5}

What is the general solution for 6sin(θ)-6=0 ?
The general solution for 6sin(θ)-6=0 is θ= pi/2+2pin