What is the general solution for sin(x)+(sqrt(3))/2 =0 ?

The general solution for sin(x)+(sqrt(3))/2 =0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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sin(x)+(sqrt(3))/2 =0

sin (x) + \frac{3}{2} = 0

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

sin (x) + \frac{3}{2} = 0

Move

\frac{3}{2}

to the right side

sin (x) + \frac{3}{2} = 0

Subtract

\frac{3}{2}

from both sides

sin (x) + \frac{3}{2} - \frac{3}{2} = 0 - \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

cos (2 θ) + cos (θ) + 1 = 0

2 sec^{2} (θ) + 3 = 4 + sec^{2} (θ)

3 cos^{2} (x) - 5 cos (x) - 2 = 0

cos (2 x) + 1 = - 2 cos (x)

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

What is the general solution for sin(x)+(sqrt(3))/2 =0 ?
The general solution for sin(x)+(sqrt(3))/2 =0 is x=(4pi)/3+2pin,x=(5pi)/3+2pin