What is the general solution for 6sin(x)+sqrt(8)=0 ?

The general solution for 6sin(x)+sqrt(8)=0 is x=-0.49088…+2pin,x=pi+0.49088…+2pin

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Popular >

6sin(x)+sqrt(8)=0

Solution

6 sin (x) + 8 = 0

Solution

x = - 0.49088 \dots + 2 πn, x = π + 0.49088 \dots + 2 πn

Degrees

x = - 28.12550 \dots^{\circ} + 36 0^{\circ} n, x = 208.12550 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (x) + 8 = 0

Simplify

6 sin (x) + 8 : 6 sin (x) + 22

6 sin (x) + 8

8 = 22

8

Prime factorization of

8 : 2^{3}

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

2

is a prime number, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2

= 2^{3}

= 2^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{2} \cdot 2

Apply radical rule:

= 2 2^{2}

Apply radical rule:

2^{2} = 2

= 22

= 6 sin (x) + 22

6 sin (x) + 22 = 0

Move

22

to the right side

6 sin (x) + 22 = 0

Subtract

22

from both sides

6 sin (x) + 22 - 22 = 0 - 22

Simplify

6 sin (x) = - 22

6 sin (x) = - 22

Divide both sides by

6

6 sin (x) = - 22

Divide both sides by

6

\frac{6 sin ( x )}{6} = \frac{- 2 2}{6}

Simplify

\frac{6 sin ( x )}{6} = \frac{- 2 2}{6}

Simplify

\frac{6 sin ( x )}{6} : sin (x)

\frac{6 sin ( x )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sin (x)

Simplify

\frac{- 2 2}{6} : - \frac{2}{3}

\frac{- 2 2}{6}

Apply the fraction rule:

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

= - \frac{2 2}{6}

Cancel the common factor:

2

= - \frac{2}{3}

sin (x) = - \frac{2}{3}

sin (x) = - \frac{2}{3}

sin (x) = - \frac{2}{3}

Apply trig inverse properties

sin (x) = - \frac{2}{3}

General solutions for

sin (x) = - \frac{2}{3}

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

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

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

Show solutions in decimal form

x = - 0.49088 \dots + 2 πn, x = π + 0.49088 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 6sin(x)+sqrt(8)=0 ?
The general solution for 6sin(x)+sqrt(8)=0 is x=-0.49088…+2pin,x=pi+0.49088…+2pin