What is the general solution for sin(x)=0.66 ?

The general solution for sin(x)=0.66 is x=0.72081…+2pin,x=pi-0.72081…+2pin

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sin(x)=0.66

sin (x) = 0.66

x = 0.72081 \dots + 2 πn, x = π - 0.72081 \dots + 2 πn

Degrees

x = 41.29987 \dots^{\circ} + 36 0^{\circ} n, x = 138.70012 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.66

Apply trig inverse properties

sin (x) = 0.66

General solutions for

sin (x) = 0.66

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

x = arcsin (0.66) + 2 πn, x = π - arcsin (0.66) + 2 πn

x = arcsin (0.66) + 2 πn, x = π - arcsin (0.66) + 2 πn

Show solutions in decimal form

x = 0.72081 \dots + 2 πn, x = π - 0.72081 \dots + 2 πn

sin (x) = 0.34

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

arcsin (3 x - 1) = \frac{1}{2}

2 cos (\frac{x}{2}) - 1 = 0

5 cos^{2} (x) - 6 cos (x) + 1 = 0

What is the general solution for sin(x)=0.66 ?
The general solution for sin(x)=0.66 is x=0.72081…+2pin,x=pi-0.72081…+2pin