What is the general solution for sin(x)=0.61366 ?

The general solution for sin(x)=0.61366 is x=0.66068…+2pin,x=pi-0.66068…+2pin

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sin(x)=0.61366

sin (x) = 0.61366

x = 0.66068 \dots + 2 πn, x = π - 0.66068 \dots + 2 πn

Degrees

x = 37.85461 \dots^{\circ} + 36 0^{\circ} n, x = 142.14538 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.61366

Apply trig inverse properties

sin (x) = 0.61366

General solutions for

sin (x) = 0.61366

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

x = arcsin (0.61366) + 2 πn, x = π - arcsin (0.61366) + 2 πn

x = arcsin (0.61366) + 2 πn, x = π - arcsin (0.61366) + 2 πn

Show solutions in decimal form

x = 0.66068 \dots + 2 πn, x = π - 0.66068 \dots + 2 πn

sin (α) = - \frac{15}{17}

sin (62.8 x + \frac{π}{4}) = sin (\frac{π}{4})

4 cos^{(2)} (x) - 4 cos (x) + 1 = 0

3 cos (2 x) = 3 sin (x)

4 cos (\frac{θ}{2}) + 3 = - 2 cos (θ)

What is the general solution for sin(x)=0.61366 ?
The general solution for sin(x)=0.61366 is x=0.66068…+2pin,x=pi-0.66068…+2pin