What is the general solution for sin(x)= 5/6 ?

The general solution for sin(x)= 5/6 is x=0.98511…+2pin,x=pi-0.98511…+2pin

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sin(x)= 5/6

sin (x) = \frac{5}{6}

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

Solution steps

sin (x) = \frac{5}{6}

Apply trig inverse properties

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

cos (2 x) - sin^{2} (x) = cos^{2} (x) + 3 cos (x)

csc (θ) = 4

2 sin (2 θ) = - 2

2 sin (2 x) = 2

2 sec (θ) + 1 = 0

What is the general solution for sin(x)= 5/6 ?
The general solution for sin(x)= 5/6 is x=0.98511…+2pin,x=pi-0.98511…+2pin