What is the general solution for 0=2sin(t) ?

The general solution for 0=2sin(t) is t=2pin,t=pi+2pin

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0=2sin(t)

0 = 2 sin (t)

t = 2 πn, t = π + 2 πn

Degrees

t = 0^{\circ} + 36 0^{\circ} n, t = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = 2 sin (t)

Switch sides

2 sin (t) = 0

Divide both sides by

2

2 sin (t) = 0

Divide both sides by

2

\frac{2 sin ( t )}{2} = \frac{0}{2}

Simplify

sin (t) = 0

sin (t) = 0

General solutions for

sin (t) = 0

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 = 0 + 2 πn, t = π + 2 πn

t = 0 + 2 πn, t = π + 2 πn

Solve

t = 0 + 2 πn : t = 2 πn

t = 0 + 2 πn

0 + 2 πn = 2 πn

t = 2 πn

t = 2 πn, t = π + 2 πn

2 sin^{2} (x) = 9 sin (x) - 4

arctan (x) + arctan (2) = arctan (7)

3 sec (x) - 1 = 2

sec (x) = 6

sin (θ) = \frac{8}{12}

What is the general solution for 0=2sin(t) ?
The general solution for 0=2sin(t) is t=2pin,t=pi+2pin