What is the general solution for sin(8x)= 1/2 ?

The general solution for sin(8x)= 1/2 is x= pi/(48)+(pin)/4 ,x=(5pi}{48}+\frac{pin)/4

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sin(8x)= 1/2

Solution

sin (8 x) = \frac{1}{2}

Solution

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{5 π}{48} + \frac{πn}{4}

Degrees

x = 3.7 5^{\circ} + 4 5^{\circ} n, x = 18.7 5^{\circ} + 4 5^{\circ} n

Solution steps

sin (8 x) = \frac{1}{2}

General solutions for

sin (8 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}

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{5 π}{6} + 2 πn

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{5 π}{6} + 2 πn

Solve

8 x = \frac{π}{6} + 2 πn : x = \frac{π}{48} + \frac{πn}{4}

8 x = \frac{π}{6} + 2 πn

Divide both sides by

8

8 x = \frac{π}{6} + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} : x

\frac{8 x}{8}

Divide the numbers:

\frac{8}{8} = 1

= x

Simplify

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8} : \frac{π}{48} + \frac{πn}{4}

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{π}{6}}{8} = \frac{π}{48}

\frac{\frac{π}{6}}{8}

Apply the fraction rule:

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

= \frac{π}{6 \cdot 8}

Multiply the numbers:

6 \cdot 8 = 48

= \frac{π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Cancel the common factor:

2

= \frac{πn}{4}

= \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

Solve

8 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{48} + \frac{πn}{4}

8 x = \frac{5 π}{6} + 2 πn

Divide both sides by

8

8 x = \frac{5 π}{6} + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} = \frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} : x

\frac{8 x}{8}

Divide the numbers:

\frac{8}{8} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8} : \frac{5 π}{48} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{5 π}{6}}{8} = \frac{5 π}{48}

\frac{\frac{5 π}{6}}{8}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 8}

Multiply the numbers:

6 \cdot 8 = 48

= \frac{5 π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Cancel the common factor:

2

= \frac{πn}{4}

= \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{5 π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{5 π}{48} + \frac{πn}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for sin(8x)= 1/2 ?
The general solution for sin(8x)= 1/2 is x= pi/(48)+(pin)/4 ,x=(5pi}{48}+\frac{pin)/4