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

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

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sin(t)=-(sqrt(2))/2

sin (t) = - \frac{2}{2}

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

Degrees

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

Solution steps

sin (t) = - \frac{2}{2}

General solutions for

sin (t) = - \frac{2}{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}

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

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

9 cos (2 θ) = 9 cos^{2} (θ) - 4

- 10 sin (x) = 0

sin (\frac{x}{5}) = 0

8400 = 624 sin (\frac{2 π}{365} t) + 8736

cos (9 x) = - 1

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