What is the general solution for 8sin(8x)+9=3 ?

The general solution for 8sin(8x)+9=3 is x=-(0.84806…)/8+(pin)/4 ,x= pi/8+(0.84806…)/8+(pin)/4

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Popular >

8sin(8x)+9=3

Solution

8 sin (8 x) + 9 = 3

Solution

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

Degrees

x = - 6.07379 \dots^{\circ} + 4 5^{\circ} n, x = 28.57379 \dots^{\circ} + 4 5^{\circ} n

Solution steps

8 sin (8 x) + 9 = 3

Move

9

to the right side

8 sin (8 x) + 9 = 3

Subtract

9

from both sides

8 sin (8 x) + 9 - 9 = 3 - 9

Simplify

8 sin (8 x) = - 6

8 sin (8 x) = - 6

Divide both sides by

8

8 sin (8 x) = - 6

Divide both sides by

8

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

Simplify

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

Simplify

\frac{8 sin ( 8 x )}{8} : sin (8 x)

\frac{8 sin ( 8 x )}{8}

Divide the numbers:

\frac{8}{8} = 1

= sin (8 x)

Simplify

\frac{- 6}{8} : - \frac{3}{4}

\frac{- 6}{8}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6}{8}

Cancel the common factor:

2

= - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

Apply trig inverse properties

sin (8 x) = - \frac{3}{4}

General solutions for

sin (8 x) = - \frac{3}{4}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

Solve

8 x = arcsin (- \frac{3}{4}) + 2 πn : x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = arcsin (- \frac{3}{4}) + 2 πn

Simplify

arcsin (- \frac{3}{4}) + 2 πn : - arcsin (\frac{3}{4}) + 2 πn

arcsin (- \frac{3}{4}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{4}) = - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4}) + 2 πn

8 x = - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

8

8 x = - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

8

\frac{8 x}{8} = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

Simplify

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

Solve

8 x = π + arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = π + arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

8

8 x = π + arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

Simplify

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

Show solutions in decimal form

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for 8sin(8x)+9=3 ?
The general solution for 8sin(8x)+9=3 is x=-(0.84806…)/8+(pin)/4 ,x= pi/8+(0.84806…)/8+(pin)/4