What is the general solution for sin(x)=(3.9)/(8.1) ?

The general solution for sin(x)=(3.9)/(8.1) is x=0.50234…+2pin,x=pi-0.50234…+2pin

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sin(x)=(3.9)/(8.1)

sin (x) = \frac{3.9}{8.1}

x = 0.50234 \dots + 2 πn, x = π - 0.50234 \dots + 2 πn

Solution steps

sin (x) = \frac{3.9}{8.1}

Apply trig inverse properties

x = arcsin (\frac{3.9}{8.1}) + 2 πn, x = π - arcsin (\frac{3.9}{8.1}) + 2 πn

Show solutions in decimal form

x = 0.50234 \dots + 2 πn, x = π - 0.50234 \dots + 2 πn

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

1 + cos (θ) = 1 - cos (θ)

4 cos (x) - 22 = 0

sin (x) cos (3 x) + cos (x) sin (3 x) = 0

4 sin^{2} (x) + 4 = 5

What is the general solution for sin(x)=(3.9)/(8.1) ?
The general solution for sin(x)=(3.9)/(8.1) is x=0.50234…+2pin,x=pi-0.50234…+2pin