What is the general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi ?

Q: What is the general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi ?

The general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(5x)+sqrt(3)=0,0<= x<= 2pi

Solution

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

Solution

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

Degrees

x = 4 8^{\circ}, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 13 2^{\circ}, x = 19 2^{\circ}, x = 20 4^{\circ}, x = 26 4^{\circ}, x = 27 6^{\circ}, x = 33 6^{\circ}, x = 34 8^{\circ}

Solution steps

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

Move

3

to the right side

2 sin (5 x) + 3 = 0

Subtract

3

from both sides

2 sin (5 x) + 3 - 3 = 0 - 3

Simplify

2 sin (5 x) = - 3

2 sin (5 x) = - 3

Divide both sides by

2

2 sin (5 x) = - 3

Divide both sides by

2

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

Simplify

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

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

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

Solve

5 x = \frac{4 π}{3} + 2 πn : x = \frac{4 π}{15} + \frac{2 πn}{5}

5 x = \frac{4 π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{4 π}{3} + 2 πn

Divide both sides by

5

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

Simplify

\frac{5 x}{5} = \frac{\frac{4 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{4 π}{3}}{5} + \frac{2 πn}{5} : \frac{4 π}{15} + \frac{2 πn}{5}

\frac{\frac{4 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{4 π}{3}}{5} = \frac{4 π}{15}

\frac{\frac{4 π}{3}}{5}

Apply the fraction rule:

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

= \frac{4 π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{4 π}{15}

= \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

Solve

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

5 x = \frac{5 π}{3} + 2 πn

Divide both sides by

5

5 x = \frac{5 π}{3} + 2 πn

Divide both sides by

5

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

Simplify

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

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

\frac{\frac{5 π}{3}}{5} = \frac{π}{3}

\frac{\frac{5 π}{3}}{5}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{5 π}{15}

Cancel the common factor:

5

= \frac{π}{3}

= \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Solutions for the range

0 \leq x \leq 2 π

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

Popular Examples

sin(2θ)=-24/25

sin (2 θ) = - \frac{24}{25}

sin(4x)+cos(4x)=1

sin (4 x) + cos (4 x) = 1

-4cos(x)=-sin^2(x)+4,0<= x<= 2pi

- 4 cos (x) = - sin^{2} (x) + 4, 0 \leq x \leq 2 π

0=cos^2(pi/(12)t)

0 = cos^{2} (\frac{π}{12} t)

sec^2(x)+2sec(x)+4=0

sec^{2} (x) + 2 sec (x) + 4 = 0

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi ?
The general solution for 2sin(5x)+sqrt(3)=0,0<= x<= 2pi is