What is the general solution for 5+6sin(x)=0 ?

The general solution for 5+6sin(x)=0 is x=-0.98511…+2pin,x=pi+0.98511…+2pin

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5+6sin(x)=0

5 + 6 sin (x) = 0

x = - 0.98511 \dots + 2 πn, x = π + 0.98511 \dots + 2 πn

Degrees

x = - 56.44269 \dots^{\circ} + 36 0^{\circ} n, x = 236.44269 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 + 6 sin (x) = 0

Move

5

to the right side

5 + 6 sin (x) = 0

Subtract

5

from both sides

5 + 6 sin (x) - 5 = 0 - 5

Simplify

6 sin (x) = - 5

6 sin (x) = - 5

Divide both sides by

6

6 sin (x) = - 5

Divide both sides by

6

\frac{6 sin ( x )}{6} = \frac{- 5}{6}

Simplify

sin (x) = - \frac{5}{6}

sin (x) = - \frac{5}{6}

Apply trig inverse properties

sin (x) = - \frac{5}{6}

General solutions for

sin (x) = - \frac{5}{6}

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

x = arcsin (- \frac{5}{6}) + 2 πn, x = π + arcsin (\frac{5}{6}) + 2 πn

x = arcsin (- \frac{5}{6}) + 2 πn, x = π + arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

x = - 0.98511 \dots + 2 πn, x = π + 0.98511 \dots + 2 πn

sin (\frac{π}{2} x) = 0

csc (\frac{θ}{2}) = - \frac{2}{3}

x, - 2 sin (x) + 2 cos (2 x) = 0

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

2 sin (3 θ) + 1 = 0

What is the general solution for 5+6sin(x)=0 ?
The general solution for 5+6sin(x)=0 is x=-0.98511…+2pin,x=pi+0.98511…+2pin