What is the general solution for 10sin(3x)=5 ?

The general solution for 10sin(3x)=5 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

10sin(3x)=5

Solution

10 sin (3 x) = 5

Solution

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{5 π}{18} + \frac{2 πn}{3}

Degrees

x = 1 0^{\circ} + 12 0^{\circ} n, x = 5 0^{\circ} + 12 0^{\circ} n

Solution steps

10 sin (3 x) = 5

Divide both sides by

10

10 sin (3 x) = 5

Divide both sides by

10

\frac{10 sin ( 3 x )}{10} = \frac{5}{10}

Simplify

sin (3 x) = \frac{1}{2}

sin (3 x) = \frac{1}{2}

General solutions for

sin (3 x) = \frac{1}{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}

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{5 π}{6} + 2 πn

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{5 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{5 π}{6} + 2 πn : x = \frac{5 π}{18} + \frac{2 πn}{3}

3 x = \frac{5 π}{6} + 2 πn

Divide both sides by

3

3 x = \frac{5 π}{6} + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{5 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{5 π}{6}}{3} + \frac{2 πn}{3} : \frac{5 π}{18} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{18}

\frac{\frac{5 π}{6}}{3}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{5 π}{18}

= \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{5 π}{18} + \frac{2 πn}{3}

Graph

Popular Examples

40^2=28^2+15^2-2(28)(15)*cos(x)

4 0^{2} = 2 8^{2} + 1 5^{2} - 2 (28) (15) \cdot cos (x)

5tan^2(x)-1=2tan^2(x)

5 tan^{2} (x) - 1 = 2 tan^{2} (x)

5sin(2x)+8cos(x)=0

5 sin (2 x) + 8 cos (x) = 0

cos^2(x)tan^2(x)csc^2(x)=sin(x)

cos^{2} (x) tan^{2} (x) csc^{2} (x) = sin (x)

cos(a)-sin(a)=cot(a)cos(a)

cos (a) - sin (a) = cot (a) cos (a)

Frequently Asked Questions (FAQ)

What is the general solution for 10sin(3x)=5 ?
The general solution for 10sin(3x)=5 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3