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

The general solution for sin(2x+pi/3)=(sqrt(3))/2 is x=pin,x=pin+pi/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

sin (2 x + \frac{π}{3}) = \frac{3}{2}

Solution

x = πn, x = πn + \frac{π}{6}

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x + \frac{π}{3}) = \frac{3}{2}

General solutions for

sin (2 x + \frac{π}{3}) = \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}

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

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

Solve

2 x + \frac{π}{3} = \frac{π}{3} + 2 πn : x = πn

2 x + \frac{π}{3} = \frac{π}{3} + 2 πn

Subtract

\frac{π}{3}

from both sides

2 x + \frac{π}{3} - \frac{π}{3} = \frac{π}{3} + 2 πn - \frac{π}{3}

Simplify

2 x = 2 πn

Divide both sides by

2

2 x = 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

x = πn

x = πn

Solve

2 x + \frac{π}{3} = \frac{2 π}{3} + 2 πn : x = πn + \frac{π}{6}

2 x + \frac{π}{3} = \frac{2 π}{3} + 2 πn

Move

\frac{π}{3}

to the right side

2 x + \frac{π}{3} = \frac{2 π}{3} + 2 πn

Subtract

\frac{π}{3}

from both sides

2 x + \frac{π}{3} - \frac{π}{3} = \frac{2 π}{3} + 2 πn - \frac{π}{3}

Simplify

2 x + \frac{π}{3} - \frac{π}{3} = \frac{2 π}{3} + 2 πn - \frac{π}{3}

Simplify

2 x + \frac{π}{3} - \frac{π}{3} : 2 x

2 x + \frac{π}{3} - \frac{π}{3}

Add similar elements:

\frac{π}{3} - \frac{π}{3} = 0

= 2 x

Simplify

\frac{2 π}{3} + 2 πn - \frac{π}{3} : 2 πn + \frac{π}{3}

\frac{2 π}{3} + 2 πn - \frac{π}{3}

Group like terms

= 2 πn - \frac{π}{3} + \frac{2 π}{3}

Combine the fractions

- \frac{π}{3} + \frac{2 π}{3} : \frac{π}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- π + 2 π}{3}

Add similar elements:

- π + 2 π = π

= \frac{π}{3}

= 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

Divide both sides by

2

2 x = 2 πn + \frac{π}{3}

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2} + \frac{\frac{π}{3}}{2}

Simplify

\frac{2 x}{2} = \frac{2 πn}{2} + \frac{\frac{π}{3}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{2 πn}{2} + \frac{\frac{π}{3}}{2} : πn + \frac{π}{6}

\frac{2 πn}{2} + \frac{\frac{π}{3}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= πn + \frac{π}{6}

x = πn + \frac{π}{6}

x = πn + \frac{π}{6}

x = πn + \frac{π}{6}

x = πn, x = πn + \frac{π}{6}

Popular Examples

6sin(20x)+1=1

6 sin (20 x) + 1 = 1

sin(x)=sqrt(1-cos(x))

sin (x) = 1 - cos (x)

tan(t)=sqrt(3)

tan (t) = 3

2cos^2(x)-9cos(x)-5=0

2 cos^{2} (x) - 9 cos (x) - 5 = 0

2sec^2(x)=3-tan(x)

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

Frequently Asked Questions (FAQ)

What is the general solution for sin(2x+pi/3)=(sqrt(3))/2 ?
The general solution for sin(2x+pi/3)=(sqrt(3))/2 is x=pin,x=pin+pi/6