What is the general solution for -2sin(x)=sqrt(3) ?

The general solution for -2sin(x)=sqrt(3) is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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-2sin(x)=sqrt(3)

- 2 sin (x) = 3

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Degrees

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

- 2 sin (x) = 3

Divide both sides by

- 2

- 2 sin (x) = 3

Divide both sides by

- 2

\frac{- 2 sin ( x )}{- 2} = \frac{3}{- 2}

Simplify

sin (x) = - \frac{3}{2}

sin (x) = - \frac{3}{2}

General solutions for

sin (x) = - \frac{3}{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{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

(\frac{2}{2}) (cos (θ) + sin (θ)) = 1

- 6 cos^{2} (θ) + 14 cos (θ) + 15 = 3 cos (θ) + 8

cos (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

2 sin (θ) = 3

2 cos (θ) = 1, 0^{\circ} \leq θ \leq 36 0^{\circ}

What is the general solution for -2sin(x)=sqrt(3) ?
The general solution for -2sin(x)=sqrt(3) is x=(4pi)/3+2pin,x=(5pi)/3+2pin