What is the general solution for 5sin(x)+2=0 ?

The general solution for 5sin(x)+2=0 is x=-0.41151…+2pin,x=pi+0.41151…+2pin

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5sin(x)+2=0

5 sin (x) + 2 = 0

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

Degrees

x = - 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 203.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sin (x) + 2 = 0

Move

2

to the right side

5 sin (x) + 2 = 0

Subtract

2

from both sides

5 sin (x) + 2 - 2 = 0 - 2

Simplify

5 sin (x) = - 2

5 sin (x) = - 2

Divide both sides by

5

5 sin (x) = - 2

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{- 2}{5}

Simplify

sin (x) = - \frac{2}{5}

sin (x) = - \frac{2}{5}

Apply trig inverse properties

sin (x) = - \frac{2}{5}

General solutions for

sin (x) = - \frac{2}{5}

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

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

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

Show solutions in decimal form

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

4 - sec^{2} (x) = 0

3 tan^{2} (x) - 9 = 0

3 cos (4 x) = 2

2 cos^{2} (x) = cos (x) + 1

4 cos (θ) + 2 = 0

What is the general solution for 5sin(x)+2=0 ?
The general solution for 5sin(x)+2=0 is x=-0.41151…+2pin,x=pi+0.41151…+2pin