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

The general solution for cos(3x)=(sqrt(3))/2 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(3x)=(sqrt(3))/2

Solution

cos (3 x) = \frac{3}{2}

Solution

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Degrees

x = 1 0^{\circ} + 12 0^{\circ} n, x = 11 0^{\circ} + 12 0^{\circ} n

Solution steps

cos (3 x) = \frac{3}{2}

General solutions for

cos (3 x) = \frac{3}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{π}{6} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{3}

3 x = \frac{π}{6} + 2 πn

Divide both sides by

3

3 x = \frac{π}{6} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{6}}{3} + \frac{2 πn}{3} : \frac{π}{18} + \frac{2 πn}{3}

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

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

Apply the fraction rule:

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

= \frac{π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

3 x = \frac{11 π}{6} + 2 πn

Divide both sides by

3

3 x = \frac{11 π}{6} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3} : \frac{11 π}{18} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} = \frac{11 π}{18}

\frac{\frac{11 π}{6}}{3}

Apply the fraction rule:

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

= \frac{11 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{11 π}{18}

= \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Popular Examples

sin(x)=cos(x)-1

sin (x) = cos (x) - 1

2sin(x)cos(x)=cos(x)

2 sin (x) cos (x) = cos (x)

tan^2(θ)-1=0

tan^{2} (θ) - 1 = 0

tan(x)-2sin(x)tan(x)=0

tan (x) - 2 sin (x) tan (x) = 0

cos(x)= 2/5

cos (x) = \frac{2}{5}

Frequently Asked Questions (FAQ)

What is the general solution for cos(3x)=(sqrt(3))/2 ?
The general solution for cos(3x)=(sqrt(3))/2 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3