What is the general solution for sin(x)=0.766 ?

The general solution for sin(x)=0.766 is x=0.87259…+2pin,x=pi-0.87259…+2pin

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sin(x)=0.766

sin (x) = 0.766

x = 0.87259 \dots + 2 πn, x = π - 0.87259 \dots + 2 πn

Degrees

x = 49.99603 \dots^{\circ} + 36 0^{\circ} n, x = 130.00396 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.766

Apply trig inverse properties

sin (x) = 0.766

General solutions for

sin (x) = 0.766

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

x = arcsin (0.766) + 2 πn, x = π - arcsin (0.766) + 2 πn

x = arcsin (0.766) + 2 πn, x = π - arcsin (0.766) + 2 πn

Show solutions in decimal form

x = 0.87259 \dots + 2 πn, x = π - 0.87259 \dots + 2 πn

sin (x) = 0.755

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

θ, ρ = (4 sin (φ) cos (θ))

sin^{2} (a) - cos^{2} (a) = 1

arcsin (x) = - 1

What is the general solution for sin(x)=0.766 ?
The general solution for sin(x)=0.766 is x=0.87259…+2pin,x=pi-0.87259…+2pin