What is the general solution for sin(x)= 1/7 ?

The general solution for sin(x)= 1/7 is x=0.14334…+2pin,x=pi-0.14334…+2pin

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sin(x)= 1/7

sin (x) = \frac{1}{7}

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn

Solution steps

sin (x) = \frac{1}{7}

Apply trig inverse properties

x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn

Show solutions in decimal form

x = 0.14334 \dots + 2 πn, x = π - 0.14334 \dots + 2 πn

tan (\frac{θ}{2}) = - 1

tan (\frac{θ}{2}) = 1

4 sin^{2} (x) cot (x) - 2 cot (x) = 0

cos (2 θ) + sin (θ) = 0

tan (θ + \frac{π}{6}) = - 3

What is the general solution for sin(x)= 1/7 ?
The general solution for sin(x)= 1/7 is x=0.14334…+2pin,x=pi-0.14334…+2pin