What is the general solution for sin(x)= 8/15 ?

The general solution for sin(x)= 8/15 is x=0.56253…+2pin,x=pi-0.56253…+2pin

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sin(x)= 8/15

sin (x) = \frac{8}{15}

x = 0.56253 \dots + 2 πn, x = π - 0.56253 \dots + 2 πn

Degrees

x = 32.23095 \dots^{\circ} + 36 0^{\circ} n, x = 147.76904 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{8}{15}

Apply trig inverse properties

sin (x) = \frac{8}{15}

General solutions for

sin (x) = \frac{8}{15}

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

x = arcsin (\frac{8}{15}) + 2 πn, x = π - arcsin (\frac{8}{15}) + 2 πn

x = arcsin (\frac{8}{15}) + 2 πn, x = π - arcsin (\frac{8}{15}) + 2 πn

Show solutions in decimal form

x = 0.56253 \dots + 2 πn, x = π - 0.56253 \dots + 2 πn

tan (x) sec (x) = 2

1 + sin (x) = 2 cos (x)

3 sin (x) = 1 + cos (x)

sin (\frac{1}{2} x) = 0

cos^{2} (x) - 2 cos (x) - 1 = 0

What is the general solution for sin(x)= 8/15 ?
The general solution for sin(x)= 8/15 is x=0.56253…+2pin,x=pi-0.56253…+2pin