What is the general solution for sin(x)= 5/12 ?

The general solution for sin(x)= 5/12 is x=0.42977…+2pin,x=pi-0.42977…+2pin

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sin(x)= 5/12

sin (x) = \frac{5}{12}

x = 0.42977 \dots + 2 πn, x = π - 0.42977 \dots + 2 πn

Solution steps

sin (x) = \frac{5}{12}

Apply trig inverse properties

x = arcsin (\frac{5}{12}) + 2 πn, x = π - arcsin (\frac{5}{12}) + 2 πn

Show solutions in decimal form

x = 0.42977 \dots + 2 πn, x = π - 0.42977 \dots + 2 πn

arctan (x) = 2

tan (2 x) = \frac{1}{3}

2 sin (θ) cos (θ) - 3 cos (θ) = 0

4 sin (θ) cos (θ) + 2 sin (θ) - 2 cos (θ) - 1 = 0

sin (θ) - 3 cos (θ) = 3

What is the general solution for sin(x)= 5/12 ?
The general solution for sin(x)= 5/12 is x=0.42977…+2pin,x=pi-0.42977…+2pin