What is the general solution for sin(x)= 8/13 ?

The general solution for sin(x)= 8/13 is x=0.66287…+2pin,x=pi-0.66287…+2pin

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sin(x)= 8/13

sin (x) = \frac{8}{13}

x = 0.66287 \dots + 2 πn, x = π - 0.66287 \dots + 2 πn

Solution steps

sin (x) = \frac{8}{13}

Apply trig inverse properties

x = arcsin (\frac{8}{13}) + 2 πn, x = π - arcsin (\frac{8}{13}) + 2 πn

Show solutions in decimal form

x = 0.66287 \dots + 2 πn, x = π - 0.66287 \dots + 2 πn

a, f = t sin (a t)

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

sin (θ - \frac{π}{4}) + 1 = 0

2 sin (x) - sin (x) = 0

cos^{2} (θ) - cos (θ) - 12 = 0

What is the general solution for sin(x)= 8/13 ?
The general solution for sin(x)= 8/13 is x=0.66287…+2pin,x=pi-0.66287…+2pin