What is the general solution for sin(x)= 8/10 ?

The general solution for sin(x)= 8/10 is x=0.92729…+2pin,x=pi-0.92729…+2pin

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sin(x)= 8/10

sin (x) = \frac{8}{10}

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

Solution steps

sin (x) = \frac{8}{10}

Cancel the common factor:

2

sin (x) = \frac{4}{5}

Apply trig inverse properties

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

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

7 cos (5 x) + 9 = 12

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

3 cot (2 x) = - 1

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

What is the general solution for sin(x)= 8/10 ?
The general solution for sin(x)= 8/10 is x=0.92729…+2pin,x=pi-0.92729…+2pin