Question

How do you solve `3sinx + 2 = 0` from 0 to 2pi?

Answer 1

`x~~5.5534576509525865` or `x~~3.8713203098167932`

Explanation:

`[1]" "3sinx+2=0`

Subtract 2 from both sides.

`[2]" "3sinx=-2`

Divide both sides by `3`.

`[3]" "sinx=-2/3`

Get the inverse sine using a calculator.

`[4]" "arcsin(-2/3)=x`

`[5]" "arcsin(-2/3)~~-0.729727656227`

Since the angle must be from `0` to `2pi`, get an angle that is coterminal with `-0.729727656227`.

`[6]" "-0.729727656227+2pi~~5.5534576509525865`

The associate angle of `5.5534576509525865` can be used as well.

`[7]" "0.729727656227+pi~~3.8713203098167932`