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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)=(-sqrt(3))/2

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

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}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

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

sec (θ) = 2

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0

cos (2 θ) = 1

sec^{2} (x) = 1

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