What is the general solution for sin(x)= 8/12 ?

The general solution for sin(x)= 8/12 is x=0.72972…+2pin,x=pi-0.72972…+2pin

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sin(x)= 8/12

sin (x) = \frac{8}{12}

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Degrees

x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{8}{12}

Cancel the common factor:

4

sin (x) = \frac{2}{3}

Apply trig inverse properties

sin (x) = \frac{2}{3}

General solutions for

sin (x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

2 cos (θ) sin (θ) + 3 cos (θ) = 0

2 - 2 sin (θ) = 4

(sin (x))^{2} = 0

tan^{2} (x) sin (x) - \frac{sin ( x )}{3} = 0

cot^{2} (a) = cos^{2} (a) (cot (a) cos (a))^{2}

What is the general solution for sin(x)= 8/12 ?
The general solution for sin(x)= 8/12 is x=0.72972…+2pin,x=pi-0.72972…+2pin