What is the general solution for 5sin(x)=1 ?

The general solution for 5sin(x)=1 is x=0.20135…+2pin,x=pi-0.20135…+2pin

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5sin(x)=1

5 sin (x) = 1

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

Solution steps

5 sin (x) = 1

Divide both sides by

5

sin (x) = \frac{1}{5}

Apply trig inverse properties

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

Show solutions in decimal form

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

5 sin (x) = 5

(1 + sin (x)) (1 + sin (x)) = cos^{2} (x)

cos (θ) = - 0.866

cos (θ) = \frac{2 5}{19}

3 csc (θ) + csc (θ) cot (θ) = 0

What is the general solution for 5sin(x)=1 ?
The general solution for 5sin(x)=1 is x=0.20135…+2pin,x=pi-0.20135…+2pin