Thread: Simple trig equation confusion

Hi, I'm a little confused over the following question:

3sin2x-1=0 on the interval XE[0,2pi]

Working it out, I got:

2x=sin-1(1/3)

Two solutions as: ~0.17 rad and ~1.4 rad

However, the answers show that there are four solutions: 0.17, 1.4, 3.31, 4.54

Most of the previous questions have only had 2 solutions and the only question I've encountered with more included cubes.

Could anyone help me figure out where the other two solutions came from and what I should be looking for in future questions of the same nature?

Thanks!

Hello, youngb11!

First, look at the interval: .

We want to be between 0 and 6.28


We have: .

Recall that the inverse sine has an infinite number of values.







We want the values between 0 and 6.28, remember?




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It's the "2" in sin 2x that causes the trouble.







But because of the "3" in 3x, we must "go around 3 times": .**

. .




And we have all the solution in the interval.


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Am I the only one aware of this?

Am I the only one who teaches this?