What is the general solution for sin(y)= 4/12 ?

The general solution for sin(y)= 4/12 is y=0.33983…+2pin,y=pi-0.33983…+2pin

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sin(y)= 4/12

sin (y) = \frac{4}{12}

y = 0.33983 \dots + 2 πn, y = π - 0.33983 \dots + 2 πn

Degrees

y = 19.47122 \dots^{\circ} + 36 0^{\circ} n, y = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (y) = \frac{4}{12}

Cancel the common factor:

4

sin (y) = \frac{1}{3}

Apply trig inverse properties

sin (y) = \frac{1}{3}

General solutions for

sin (y) = \frac{1}{3}

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

y = arcsin (\frac{1}{3}) + 2 πn, y = π - arcsin (\frac{1}{3}) + 2 πn

y = arcsin (\frac{1}{3}) + 2 πn, y = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

y = 0.33983 \dots + 2 πn, y = π - 0.33983 \dots + 2 πn

x, 2 y sin (x) = 0

2 sin^{2} (\frac{θ}{2}) - 2 cos^{2} (θ) = 0

- 14 sin (x) + 14 cos (2 x) = 0

2 cos (2 x) + 2 = 0, 0 \leq x \leq 2 π

sin (x) = \frac{10}{25}

What is the general solution for sin(y)= 4/12 ?
The general solution for sin(y)= 4/12 is y=0.33983…+2pin,y=pi-0.33983…+2pin