What is the general solution for sin(x)=-12/13 ?

The general solution for sin(x)=-12/13 is x=-1.17600…+2pin,x=pi+1.17600…+2pin

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sin(x)=-12/13

sin (x) = - \frac{12}{13}

x = - 1.17600 \dots + 2 πn, x = π + 1.17600 \dots + 2 πn

Solution steps

sin (x) = - \frac{12}{13}

Apply trig inverse properties

x = arcsin (- \frac{12}{13}) + 2 πn, x = π + arcsin (\frac{12}{13}) + 2 πn

Show solutions in decimal form

x = - 1.17600 \dots + 2 πn, x = π + 1.17600 \dots + 2 πn

2 sin^{2} (x) + 7 sin (x) - 4 = 0

cos (\frac{5 π}{4} + x) + sin (\frac{5 π}{4} - x) = 0

cos (2 x) + sin (2 x) = 1

θ, sin (θ) = \frac{1}{2}

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

What is the general solution for sin(x)=-12/13 ?
The general solution for sin(x)=-12/13 is x=-1.17600…+2pin,x=pi+1.17600…+2pin