What is the general solution for 5sin(x)-1=0 ?

The general solution for 5sin(x)-1=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin

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5sin(x)-1=0

5 sin (x) - 1 = 0

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

Solution steps

5 sin (x) - 1 = 0

Move

1

to the right side

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

sec^{2} (x) = 4 tan (x) - 2

sin (x) = 2 sin (x) cos (x)

4 sin^{3} (x) + 2 sin^{2} (x) - 2 sin (x) - 1 = 0

3 tan^{2} (θ) = 7 sec (θ) - 5

sin (x^{2} + 1) - cos (x^{2} + 1) = 0

What is the general solution for 5sin(x)-1=0 ?
The general solution for 5sin(x)-1=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin