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

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

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sin(2y)=0

sin (2 y) = 0

y = πn, y = \frac{π}{2} + πn

Degrees

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

Solution steps

sin (2 y) = 0

General solutions for

sin (2 y) = 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 y = 0 + 2 πn, 2 y = π + 2 πn

2 y = 0 + 2 πn, 2 y = π + 2 πn

Solve

2 y = 0 + 2 πn : y = πn

2 y = 0 + 2 πn

0 + 2 πn = 2 πn

2 y = 2 πn

Divide both sides by

2

2 y = 2 πn

Divide both sides by

2

\frac{2 y}{2} = \frac{2 πn}{2}

Simplify

y = πn

y = πn

Solve

2 y = π + 2 πn : y = \frac{π}{2} + πn

2 y = π + 2 πn

Divide both sides by

2

2 y = π + 2 πn

Divide both sides by

2

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

Simplify

y = \frac{π}{2} + πn

y = \frac{π}{2} + πn

y = πn, y = \frac{π}{2} + πn

7 sin^{2} (θ) - 15 sin (θ) + 8 = 0

sin (5 t) = 0

cos (x) = 0, - π \leq x \leq π

sin^{2} (x) + cos (x) = 2

sin (θ) = - \frac{4}{5}, \frac{7 π}{2} \leq θ < 4 π, cos (2 θ)

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