What is the general solution for sin(5x)=(sqrt(3))/2 ?

The general solution for sin(5x)=(sqrt(3))/2 is x= pi/(15)+(2pin)/5 ,x=(2pi}{15}+\frac{2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(5x)=(sqrt(3))/2

Solution

sin (5 x) = \frac{3}{2}

Solution

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{2 π}{15} + \frac{2 πn}{5}

Degrees

x = 1 2^{\circ} + 7 2^{\circ} n, x = 2 4^{\circ} + 7 2^{\circ} n

Solution steps

sin (5 x) = \frac{3}{2}

General solutions for

sin (5 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}

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

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

Solve

5 x = \frac{π}{3} + 2 πn : x = \frac{π}{15} + \frac{2 πn}{5}

5 x = \frac{π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{π}{3} + 2 πn

Divide both sides by

5

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

Simplify

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

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5} : \frac{π}{15} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} = \frac{π}{15}

\frac{\frac{π}{3}}{5}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{π}{15}

= \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

Solve

5 x = \frac{2 π}{3} + 2 πn : x = \frac{2 π}{15} + \frac{2 πn}{5}

5 x = \frac{2 π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{2 π}{3} + 2 πn

Divide both sides by

5

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

Simplify

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

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{2 π}{3}}{5} + \frac{2 πn}{5} : \frac{2 π}{15} + \frac{2 πn}{5}

\frac{\frac{2 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{2 π}{3}}{5} = \frac{2 π}{15}

\frac{\frac{2 π}{3}}{5}

Apply the fraction rule:

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

= \frac{2 π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{2 π}{15}

= \frac{2 π}{15} + \frac{2 πn}{5}

x = \frac{2 π}{15} + \frac{2 πn}{5}

x = \frac{2 π}{15} + \frac{2 πn}{5}

x = \frac{2 π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{2 π}{15} + \frac{2 πn}{5}

Popular Examples

sin^2(θ)-cos^2(θ)=-1

sin^{2} (θ) - cos^{2} (θ) = - 1

cos^2(x)-4cos(x)=0

cos^{2} (x) - 4 cos (x) = 0

solvefor x,sin(x)+cot(x)cos(x)= 1/f solve for

x, sin (x) + cot (x) cos (x) = \frac{1}{f}

1/(sin(x))=2

\frac{1}{sin ( x )} = 2

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

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

Frequently Asked Questions (FAQ)

What is the general solution for sin(5x)=(sqrt(3))/2 ?
The general solution for sin(5x)=(sqrt(3))/2 is x= pi/(15)+(2pin)/5 ,x=(2pi}{15}+\frac{2pin)/5