What is the general solution for sin(a)=0.2315 ?

The general solution for sin(a)=0.2315 is a=0.23361…+2pin,a=pi-0.23361…+2pin

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sin(a)=0.2315

sin (a) = 0.2315

a = 0.23361 \dots + 2 πn, a = π - 0.23361 \dots + 2 πn

Degrees

a = 13.38539 \dots^{\circ} + 36 0^{\circ} n, a = 166.61460 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = 0.2315

Apply trig inverse properties

sin (a) = 0.2315

General solutions for

sin (a) = 0.2315

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

a = arcsin (0.2315) + 2 πn, a = π - arcsin (0.2315) + 2 πn

a = arcsin (0.2315) + 2 πn, a = π - arcsin (0.2315) + 2 πn

Show solutions in decimal form

a = 0.23361 \dots + 2 πn, a = π - 0.23361 \dots + 2 πn

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sin (x) sin^{3} (x) - sin^{5} (x) sin^{3} (x) = 0

5 sin^{2} (x) = 2 sin (x)

3 cos^{2} (x) + 5 sin (x) - 4 = 0

x, d^{2} + 3 d + 2 y = 4 cos^{2} (x)

What is the general solution for sin(a)=0.2315 ?
The general solution for sin(a)=0.2315 is a=0.23361…+2pin,a=pi-0.23361…+2pin