What is the general solution for 9sin(x-0.5pi)+8=0 ?

The general solution for 9sin(x-0.5pi)+8=0 is x=-1.09491…+2pin+0.5pi,x=1.5pi+2pin+1.09491…

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9sin(x-0.5pi)+8=0

Solution

9 sin (x - 0.5 π) + 8 = 0

Solution

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

Degrees

x = 27.26604 \dots^{\circ} + 36 0^{\circ} n, x = 332.73395 \dots^{\circ} + 36 0^{\circ} n

Solution steps

9 sin (x - 0.5 π) + 8 = 0

Move

8

to the right side

9 sin (x - 0.5 π) + 8 = 0

Subtract

8

from both sides

9 sin (x - 0.5 π) + 8 - 8 = 0 - 8

Simplify

9 sin (x - 0.5 π) = - 8

9 sin (x - 0.5 π) = - 8

Divide both sides by

9

9 sin (x - 0.5 π) = - 8

Divide both sides by

9

\frac{9 sin ( x - 0.5 π )}{9} = \frac{- 8}{9}

Simplify

sin (x - 0.5 π) = - \frac{8}{9}

sin (x - 0.5 π) = - \frac{8}{9}

Apply trig inverse properties

sin (x - 0.5 π) = - \frac{8}{9}

General solutions for

sin (x - 0.5 π) = - \frac{8}{9}

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

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn, x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn, x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Solve

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn : x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn

Simplify

arcsin (- \frac{8}{9}) + 2 πn : - arcsin (\frac{8}{9}) + 2 πn

arcsin (- \frac{8}{9}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{8}{9}) = - arcsin (\frac{8}{9})

= - arcsin (\frac{8}{9}) + 2 πn

x - 0.5 π = - arcsin (\frac{8}{9}) + 2 πn

Move

0.5 π

to the right side

x - 0.5 π = - arcsin (\frac{8}{9}) + 2 πn

Add

0.5 π

to both sides

x - 0.5 π + 0.5 π = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplify

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Solve

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn : x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Move

0.5 π

to the right side

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Add

0.5 π

to both sides

x - 0.5 π + 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplify

x - 0.5 π + 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Simplify

x - 0.5 π + 0.5 π : x

x - 0.5 π + 0.5 π

Add similar elements:

- 0.5 π + 0.5 π = 0

= x

Simplify

π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π : 1.5 π + 2 πn + arcsin (\frac{8}{9})

π + arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Group like terms

= π + 0.5 π + 2 πn + arcsin (\frac{8}{9})

Add similar elements:

π + 0.5 π = 1.5 π

= 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π, x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

Show solutions in decimal form

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for 9sin(x-0.5pi)+8=0 ?
The general solution for 9sin(x-0.5pi)+8=0 is x=-1.09491…+2pin+0.5pi,x=1.5pi+2pin+1.09491…