What is the general solution for sin(x)= 6/7 ?

The general solution for sin(x)= 6/7 is x=1.02969…+2pin,x=pi-1.02969…+2pin

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sin(x)= 6/7

sin (x) = \frac{6}{7}

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

Solution steps

sin (x) = \frac{6}{7}

Apply trig inverse properties

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

Show solutions in decimal form

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

x, sin (x) = - \frac{1}{2}

sin (\frac{θ}{2}) = \frac{1}{2}

4 cos (θ) - 22 = 0

4 cos (4 x) = 0

4 sin^{3} (x) - 3 sin (x) = 0

What is the general solution for sin(x)= 6/7 ?
The general solution for sin(x)= 6/7 is x=1.02969…+2pin,x=pi-1.02969…+2pin