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

Question

8379 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-28T16:16:04

$x~~5.5534576509525865$ or $x~~3.8713203098167932$

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

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.

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

How do you solve 3sinx + 2 = 03sinx + 2 = 0 from 0 to 2pi?