What is the general solution for solvefor x,2ysin(x)=0 ?

The general solution for solvefor x,2ysin(x)=0 is x=2pin,x=pi+2pin

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solvefor x,2ysin(x)=0

solve for

x, 2 y sin (x) = 0

x = 2 πn, x = π + 2 πn

Degrees

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

Solution steps

2 y sin (x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

sin (x) = 0

General solutions for

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

2 sin^{2} (\frac{θ}{2}) - 2 cos^{2} (θ) = 0

- 14 sin (x) + 14 cos (2 x) = 0

2 cos (2 x) + 2 = 0, 0 \leq x \leq 2 π

sin (x) = \frac{10}{25}

\frac{tan ( x )}{sin ( x )} = cos (x)

What is the general solution for solvefor x,2ysin(x)=0 ?
The general solution for solvefor x,2ysin(x)=0 is x=2pin,x=pi+2pin