What is the general solution for sin(x)=-sqrt(1/2) ?

The general solution for sin(x)=-sqrt(1/2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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sin(x)=-sqrt(1/2)

sin (x) = - \frac{1}{2}

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Degrees

x = 22 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - \frac{1}{2}

General solutions for

sin (x) = - \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

tan (x) - \frac{3}{3} = 0

tan (2 θ) = 0.5714

\frac{3}{1 + cos ( θ )} = 1 + 2 cos (θ)

4 - 4 cos (θ) = 6

sin^{2} (θ) - 2 sin (θ) + 1 = 0

What is the general solution for sin(x)=-sqrt(1/2) ?
The general solution for sin(x)=-sqrt(1/2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin