What is the general solution for sin(x)=0.86 ?

The general solution for sin(x)=0.86 is x=1.03526…+2pin,x=pi-1.03526…+2pin

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sin(x)=0.86

sin (x) = 0.86

x = 1.03526 \dots + 2 πn, x = π - 1.03526 \dots + 2 πn

Degrees

x = 59.31658 \dots^{\circ} + 36 0^{\circ} n, x = 120.68341 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.86

Apply trig inverse properties

sin (x) = 0.86

General solutions for

sin (x) = 0.86

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

x = arcsin (0.86) + 2 πn, x = π - arcsin (0.86) + 2 πn

x = arcsin (0.86) + 2 πn, x = π - arcsin (0.86) + 2 πn

Show solutions in decimal form

x = 1.03526 \dots + 2 πn, x = π - 1.03526 \dots + 2 πn

2 sin (2 θ) + 3 = 0

sin^{2} (x) + 4 sin (x) + 3 = 0

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

4 cos (2 θ) + 3 cos (θ) + 4 = - 3 cos (θ) - 1

cos (θ - \frac{π}{4}) - 1 = 0

What is the general solution for sin(x)=0.86 ?
The general solution for sin(x)=0.86 is x=1.03526…+2pin,x=pi-1.03526…+2pin