What is the general solution for sin(θ)= 1/2 ,0<= θ<= 4pi ?

The general solution for sin(θ)= 1/2 ,0<= θ<= 4pi is θ= pi/6 ,θ=(5pi)/6 ,θ=(13pi)/6 ,θ=(17pi)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sin(θ)= 1/2 ,0<= θ<= 4pi

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

θ = \frac{π}{6}, θ = \frac{5 π}{6}, θ = \frac{13 π}{6}, θ = \frac{17 π}{6}

Degrees

θ = 3 0^{\circ}, θ = 15 0^{\circ}, θ = 39 0^{\circ}, θ = 51 0^{\circ}

Solution steps

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

General solutions for

sin (θ) = \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}

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

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

Solutions for the range

0 \leq θ \leq 4 π

θ = \frac{π}{6}, θ = \frac{5 π}{6}, θ = \frac{13 π}{6}, θ = \frac{17 π}{6}

What is the general solution for sin(θ)= 1/2 ,0<= θ<= 4pi ?
The general solution for sin(θ)= 1/2 ,0<= θ<= 4pi is θ= pi/6 ,θ=(5pi)/6 ,θ=(13pi)/6 ,θ=(17pi)/6