What is the general solution for sin(x)=0.25 ?

The general solution for sin(x)=0.25 is x=0.25268…+2pin,x=pi-0.25268…+2pin

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sin(x)=0.25

sin (x) = 0.25

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Degrees

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.25

Apply trig inverse properties

sin (x) = 0.25

General solutions for

sin (x) = 0.25

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

x = arcsin (0.25) + 2 πn, x = π - arcsin (0.25) + 2 πn

x = arcsin (0.25) + 2 πn, x = π - arcsin (0.25) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

tan (x) (tan (x) + 1) = 0

cos (θ) = sin (2 θ)

θ, tan (θ) = 1

sec (x) csc (x) - 2 csc (x) = 0

csc (3 θ) = 6 sin (3 θ), 0 < θ < 2 π

What is the general solution for sin(x)=0.25 ?
The general solution for sin(x)=0.25 is x=0.25268…+2pin,x=pi-0.25268…+2pin