What is the general solution for 9sin(18x)+11=2 ?

The general solution for 9sin(18x)+11=2 is x= pi/(12)+(pin)/9

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Popular >

9sin(18x)+11=2

Solution

9 sin (18 x) + 11 = 2

Solution

x = \frac{π}{12} + \frac{πn}{9}

Degrees

x = 1 5^{\circ} + 2 0^{\circ} n

Solution steps

9 sin (18 x) + 11 = 2

Move

11

to the right side

9 sin (18 x) + 11 = 2

Subtract

11

from both sides

9 sin (18 x) + 11 - 11 = 2 - 11

Simplify

9 sin (18 x) = - 9

9 sin (18 x) = - 9

Divide both sides by

9

9 sin (18 x) = - 9

Divide both sides by

9

\frac{9 sin ( 18 x )}{9} = \frac{- 9}{9}

Simplify

sin (18 x) = - 1

sin (18 x) = - 1

General solutions for

sin (18 x) = - 1

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}

18 x = \frac{3 π}{2} + 2 πn

18 x = \frac{3 π}{2} + 2 πn

Solve

18 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{12} + \frac{πn}{9}

18 x = \frac{3 π}{2} + 2 πn

Divide both sides by

18

18 x = \frac{3 π}{2} + 2 πn

Divide both sides by

18

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

Simplify

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

Simplify

\frac{18 x}{18} : x

\frac{18 x}{18}

Divide the numbers:

\frac{18}{18} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{18} + \frac{2 πn}{18} : \frac{π}{12} + \frac{πn}{9}

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

\frac{\frac{3 π}{2}}{18} = \frac{π}{12}

\frac{\frac{3 π}{2}}{18}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 18}

Multiply the numbers:

2 \cdot 18 = 36

= \frac{3 π}{36}

Cancel the common factor:

3

= \frac{π}{12}

\frac{2 πn}{18} = \frac{πn}{9}

\frac{2 πn}{18}

Cancel the common factor:

2

= \frac{πn}{9}

= \frac{π}{12} + \frac{πn}{9}

x = \frac{π}{12} + \frac{πn}{9}

x = \frac{π}{12} + \frac{πn}{9}

x = \frac{π}{12} + \frac{πn}{9}

x = \frac{π}{12} + \frac{πn}{9}

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Frequently Asked Questions (FAQ)

What is the general solution for 9sin(18x)+11=2 ?
The general solution for 9sin(18x)+11=2 is x= pi/(12)+(pin)/9