What is the general solution for sin(x)= 6/8 ?

The general solution for sin(x)= 6/8 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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sin(x)= 6/8

sin (x) = \frac{6}{8}

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

sin (x) = \frac{6}{8}

Cancel the common factor:

2

sin (x) = \frac{3}{4}

Apply trig inverse properties

x = arcsin (\frac{3}{4}) + 2 πn, x = π - arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

tan (x) = 2 + tan (3 x)

2 sin (x) - 3 = 0

sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

5 sin (x) = cos (x) - 4

tan (x) - 3 = 0

What is the general solution for sin(x)= 6/8 ?
The general solution for sin(x)= 6/8 is x=0.84806…+2pin,x=pi-0.84806…+2pin