What is the general solution for sin(t)=-1 ?

The general solution for sin(t)=-1 is t=(3pi)/2+2pin

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sin(t)=-1

sin (t) = - 1

t = \frac{3 π}{2} + 2 πn

Degrees

t = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (t) = - 1

General solutions for

sin (t) = - 1

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{3 π}{2} + 2 πn

t = \frac{3 π}{2} + 2 πn

sin (3 x) = 1, 0 \leq x \leq 2 π

x, z = arcsin (\frac{x}{x ^{2} + y ^{2}})

cos (θ) (2 cos (θ) + 1) = 0

2 cot (x) - 2 = 0

1 - 2 sin (x) = 0

What is the general solution for sin(t)=-1 ?
The general solution for sin(t)=-1 is t=(3pi)/2+2pin