Find x in radians using [0,2pi] | Sin(3x)= -0.1658 | Step-by-Step Solution"

[darshanpatel]

Homework Statement

Find x in radians using [0,2pi]

Sin(3x)= -0.1658

Homework Equations

-None-

The Attempt at a Solution

3x=Sin^-1(-0.1658)

x=sin^-1(-0.1658)/3

x= -0.055523061

The teacher gave me a whole page to do the problem, so I don't know if there should be more work or not. Not positive if this answer is correct also.

 

[Villyer]

I believe that there should be 6 answers to this equation.

 

[darshanpatel]

Ok, could you help me get them? I don't understand this question at all.

 

[Villyer]

Your work was all right, and your answer is in fact a zero of the equation. But it doesn't lie in the domain you are looking for.

When solving these equations, think of the unit circle.
sin and the height of the circle are related. So solving for when the sin(x) = -.1658, can you see how many solutions are?

 

[Chestermiller]

Ok, could you help me get them? I don't understand this question at all.

Here are some hints:

sin (pi - θ) = sinθ
sin(2n*pi-θ)=-sinθ
plus other similar relations

chet

 

[darshanpatel]

I still don't understand. If I could get the answers, I could try back-tracking to get the work and understand how to do it.

 

[Muphrid]

You need to think logically about your answer; it's not in the range 0 to 2pi. You have a negative angle that has this sine. What positive angles in the range 0 to 2pi will have that sine?