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

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

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sin(2w)=0

sin (2 w) = 0

w = πn, w = \frac{π}{2} + πn

Degrees

w = 0^{\circ} + 18 0^{\circ} n, w = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 w) = 0

General solutions for

sin (2 w) = 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}

2 w = 0 + 2 πn, 2 w = π + 2 πn

2 w = 0 + 2 πn, 2 w = π + 2 πn

Solve

2 w = 0 + 2 πn : w = πn

2 w = 0 + 2 πn

0 + 2 πn = 2 πn

2 w = 2 πn

Divide both sides by

2

2 w = 2 πn

Divide both sides by

2

\frac{2 w}{2} = \frac{2 πn}{2}

Simplify

w = πn

w = πn

Solve

2 w = π + 2 πn : w = \frac{π}{2} + πn

2 w = π + 2 πn

Divide both sides by

2

2 w = π + 2 πn

Divide both sides by

2

\frac{2 w}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplify

w = \frac{π}{2} + πn

w = \frac{π}{2} + πn

w = πn, w = \frac{π}{2} + πn

4 sin^{(2)} (θ) - 3 = 0

3 cos (5 t) = 0

cos^{2} (9 0^{\circ} - θ) = 1872

cos (x) - cos (x) = 0

sin (x + 1) = cos (x)

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