What is the general solution for sin(x)= 1000/2022 ?

The general solution for sin(x)= 1000/2022 is x=0.51732…+2pin,x=pi-0.51732…+2pin

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sin(x)= 1000/2022

sin (x) = \frac{1000}{2022}

x = 0.51732 \dots + 2 πn, x = π - 0.51732 \dots + 2 πn

Solution steps

sin (x) = \frac{1000}{2022}

Cancel the common factor:

2

sin (x) = \frac{500}{1011}

Apply trig inverse properties

x = arcsin (\frac{500}{1011}) + 2 πn, x = π - arcsin (\frac{500}{1011}) + 2 πn

Show solutions in decimal form

x = 0.51732 \dots + 2 πn, x = π - 0.51732 \dots + 2 πn

x, arcsin (x) = ln (y)

cos (x) - 1 = 2 cos (x)

cos (5 x) = - 1, 0 \leq x < 2 π

sinh (x) = - 1

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

What is the general solution for sin(x)= 1000/2022 ?
The general solution for sin(x)= 1000/2022 is x=0.51732…+2pin,x=pi-0.51732…+2pin