What is the general solution for 1=2sin(x) ?

The general solution for 1=2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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1=2sin(x)

1 = 2 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

1 = 2 sin (x)

Switch sides

2 sin (x) = 1

Divide both sides by

2

2 sin (x) = 1

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

Simplify

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

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 = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

sin (2 x - \frac{π}{4}) = 0

7 sin^{2} (θ) - 4 sin (θ) = 3

tan (θ) - cot (θ) = 0

csc^{3} (x) + csc^{2} (x) = \frac{4}{3} csc (x) + \frac{4}{3}

What is the general solution for 1=2sin(x) ?
The general solution for 1=2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin