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

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

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0=sin(y)

0 = sin (y)

y = 2 πn, y = π + 2 πn

Degrees

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

Solution steps

0 = sin (y)

Switch sides

sin (y) = 0

General solutions for

sin (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}

y = 0 + 2 πn, y = π + 2 πn

y = 0 + 2 πn, y = π + 2 πn

Solve

y = 0 + 2 πn : y = 2 πn

y = 0 + 2 πn

0 + 2 πn = 2 πn

y = 2 πn

y = 2 πn, y = π + 2 πn

\frac{cot ( x )}{sec ( x )} = sin (x)

tan^{2} (x) - sec^{2} (x) = cos (- x)

sec^{2} (θ) tan (θ) = 2 tan (θ), 0 \leq θ \leq 2 π

cos (2 x) cos (x) - sin (2 x) sin (x) = \frac{2}{2}

- 2 + cos (θ) = - 2 + \frac{6}{5} \cdot cos (θ)

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