What is the general solution for 2-3sin(θ+(4pi)/3)=2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2-3sin(θ+(4pi)/3)=2

Solution

2 - 3 sin (θ + \frac{4 π}{3}) = 2

Solution

θ = 2 πn - \frac{4 π}{3}, θ = π + 2 πn - \frac{4 π}{3}

Degrees

θ = - 24 0^{\circ} + 36 0^{\circ} n, θ = - 6 0^{\circ} + 36 0^{\circ} n

Solution steps

2 - 3 sin (θ + \frac{4 π}{3}) = 2

Subtract

2

from both sides

2 - 3 sin (θ + \frac{4 π}{3}) - 2 = 2 - 2

Simplify

- 3 sin (θ + \frac{4 π}{3}) = 0

Divide both sides by

- 3

- 3 sin (θ + \frac{4 π}{3}) = 0

Divide both sides by

- 3

\frac{- 3 sin ( θ + \frac{4 π}{3} )}{- 3} = \frac{0}{- 3}

Simplify

sin (θ + \frac{4 π}{3}) = 0

sin (θ + \frac{4 π}{3}) = 0

General solutions for

sin (θ + \frac{4 π}{3}) = 0

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{4 π}{3} = 0 + 2 πn, θ + \frac{4 π}{3} = π + 2 πn

θ + \frac{4 π}{3} = 0 + 2 πn, θ + \frac{4 π}{3} = π + 2 πn

Solve

θ + \frac{4 π}{3} = 0 + 2 πn : θ = 2 πn - \frac{4 π}{3}

θ + \frac{4 π}{3} = 0 + 2 πn

0 + 2 πn = 2 πn

θ + \frac{4 π}{3} = 2 πn

Move

\frac{4 π}{3}

to the right side

θ + \frac{4 π}{3} = 2 πn

Subtract

\frac{4 π}{3}

from both sides

θ + \frac{4 π}{3} - \frac{4 π}{3} = 2 πn - \frac{4 π}{3}

Simplify

θ = 2 πn - \frac{4 π}{3}

θ = 2 πn - \frac{4 π}{3}

Solve

θ + \frac{4 π}{3} = π + 2 πn : θ = π + 2 πn - \frac{4 π}{3}

θ + \frac{4 π}{3} = π + 2 πn

Move

\frac{4 π}{3}

to the right side

θ + \frac{4 π}{3} = π + 2 πn

Subtract

\frac{4 π}{3}

from both sides

θ + \frac{4 π}{3} - \frac{4 π}{3} = π + 2 πn - \frac{4 π}{3}

Simplify

θ = π + 2 πn - \frac{4 π}{3}

θ = π + 2 πn - \frac{4 π}{3}

θ = 2 πn - \frac{4 π}{3}, θ = π + 2 πn - \frac{4 π}{3}

Popular Examples

tan(θ)= 2/6

tan (θ) = \frac{2}{6}

4+3cos(x)=0

4 + 3 cos (x) = 0

3sin^2(θ)-sin(θ)-4=0

3 sin^{2} (θ) - sin (θ) - 4 = 0

tan^2(x)=sin(x)sec(x)

tan^{2} (x) = sin (x) sec (x)

cos(x)=-6544

cos (x) = - 6544

Frequently Asked Questions (FAQ)

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