What is the general solution for sin(x)=0.9 ?

The general solution for sin(x)=0.9 is x=1.11976…+2pin,x=pi-1.11976…+2pin

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sin(x)=0.9

sin (x) = 0.9

x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

Degrees

x = 64.15806 \dots^{\circ} + 36 0^{\circ} n, x = 115.84193 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.9

Apply trig inverse properties

sin (x) = 0.9

General solutions for

sin (x) = 0.9

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (0.9) + 2 πn, x = π - arcsin (0.9) + 2 πn

x = arcsin (0.9) + 2 πn, x = π - arcsin (0.9) + 2 πn

Show solutions in decimal form

x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

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

cos^{2} (θ) = \frac{1}{2}

sin (x) = \frac{8}{17}

sin (x) = \frac{1}{2}, 0 \leq x \leq 2 π

2 cos^{2} (x) - 5 cos (x) - 3 = 0

What is the general solution for sin(x)=0.9 ?
The general solution for sin(x)=0.9 is x=1.11976…+2pin,x=pi-1.11976…+2pin