What is the general solution for 9(sin(x)-0.6pi)+8=0 ?

The general solution for 9(sin(x)-0.6pi)+8=0 is x=1.48207…+2pin,x=pi-1.48207…+2pin

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Popular Trigonometry >

9(sin(x)-0.6pi)+8=0

Solution

9 (sin (x) - 0.6 π) + 8 = 0

Solution

x = 1.48207 \dots + 2 πn, x = π - 1.48207 \dots + 2 πn

Degrees

x = 84.91655 \dots^{\circ} + 36 0^{\circ} n, x = 95.08344 \dots^{\circ} + 36 0^{\circ} n

Solution steps

9 (sin (x) - 0.6 π) + 8 = 0

Move

8

to the right side

9 (sin (x) - 0.6 π) + 8 = 0

Subtract

8

from both sides

9 (sin (x) - 0.6 π) + 8 - 8 = 0 - 8

Simplify

9 (sin (x) - 0.6 π) = - 8

9 (sin (x) - 0.6 π) = - 8

Divide both sides by

9

9 (sin (x) - 0.6 π) = - 8

Divide both sides by

9

\frac{9 ( sin ( x ) - 0.6 π )}{9} = \frac{- 8}{9}

Simplify

sin (x) - 1.88495 \dots = - \frac{8}{9}

sin (x) - 1.88495 \dots = - \frac{8}{9}

Move

1.88495 \dots

to the right side

sin (x) - 1.88495 \dots = - \frac{8}{9}

Add

1.88495 \dots

to both sides

sin (x) - 1.88495 \dots + 1.88495 \dots = - \frac{8}{9} + 1.88495 \dots

Simplify

sin (x) - 1.88495 \dots + 1.88495 \dots = - \frac{8}{9} + 1.88495 \dots

Simplify

sin (x) - 1.88495 \dots + 1.88495 \dots : sin (x)

sin (x) - 1.88495 \dots + 1.88495 \dots

Add similar elements:

- 1.88495 \dots + 1.88495 \dots = 0

= sin (x)

Simplify

- \frac{8}{9} + 1.88495 \dots : 0.99606 \dots

- \frac{8}{9} + 1.88495 \dots

Convert element to a decimal form

\frac{8}{9} = 0.88888 \dots

= - 0.88888 \dots + 1.88495 \dots

Add/Subtract the numbers:

- 0.88888 \dots + 1.88495 \dots = 0.99606 \dots

= 0.99606 \dots

sin (x) = 0.99606 \dots

sin (x) = 0.99606 \dots

sin (x) = 0.99606 \dots

Apply trig inverse properties

sin (x) = 0.99606 \dots

General solutions for

sin (x) = 0.99606 \dots

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

x = arcsin (0.99606 \dots) + 2 πn, x = π - arcsin (0.99606 \dots) + 2 πn

x = arcsin (0.99606 \dots) + 2 πn, x = π - arcsin (0.99606 \dots) + 2 πn

Show solutions in decimal form

x = 1.48207 \dots + 2 πn, x = π - 1.48207 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 9(sin(x)-0.6pi)+8=0 ?
The general solution for 9(sin(x)-0.6pi)+8=0 is x=1.48207…+2pin,x=pi-1.48207…+2pin