What is the general solution for sin(x)=0.53 ?

The general solution for sin(x)=0.53 is x=0.55860…+2pin,x=pi-0.55860…+2pin

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sin(x)=0.53

sin (x) = 0.53

x = 0.55860 \dots + 2 πn, x = π - 0.55860 \dots + 2 πn

Degrees

x = 32.00545 \dots^{\circ} + 36 0^{\circ} n, x = 147.99454 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.53

Apply trig inverse properties

sin (x) = 0.53

General solutions for

sin (x) = 0.53

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

x = arcsin (0.53) + 2 πn, x = π - arcsin (0.53) + 2 πn

x = arcsin (0.53) + 2 πn, x = π - arcsin (0.53) + 2 πn

Show solutions in decimal form

x = 0.55860 \dots + 2 πn, x = π - 0.55860 \dots + 2 πn

2 cos (2 θ) = 2

2 + sin (x) = 0

sin (x) = 0.45

sin (x) = 0.42

- 3 cos (θ) + 3 = 2 sin^{2} (θ)

What is the general solution for sin(x)=0.53 ?
The general solution for sin(x)=0.53 is x=0.55860…+2pin,x=pi-0.55860…+2pin