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

The general solution for 3sin(x)+sqrt(3)=sin(x) 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 >

3sin(x)+sqrt(3)=sin(x)

3 sin (x) + 3 = sin (x)

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

3 sin (x) + 3 = sin (x)

Solve by substitution

3 sin (x) + 3 = sin (x)

Let:

sin (x) = u

3 u + 3 = u

3 u + 3 = u : u = - \frac{3}{2}

3 u + 3 = u

Move

3

to the right side

3 u + 3 = u

Subtract

3

from both sides

3 u + 3 - 3 = u - 3

Simplify

3 u = u - 3

3 u = u - 3

Move

u

to the left side

3 u = u - 3

Subtract

u

from both sides

3 u - u = u - 3 - u

Simplify

2 u = - 3

2 u = - 3

Divide both sides by

2

2 u = - 3

Divide both sides by

2

\frac{2 u}{2} = \frac{- 3}{2}

Simplify

u = - \frac{3}{2}

u = - \frac{3}{2}

Substitute back

u = sin (x)

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

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

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

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

Combine all the solutions

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

4 sec^{2} (x) - 7 tan^{2} (x) = 3

sin (3 x) = cos (2 x)

3 csc^{2} (θ) - 4 = 0

sin (x) = \frac{7}{9}

2 cos (t) = 0

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