# Trigonometric Equations

Hi So, this is what I have to solve: 2sin2x - sin x = 0

I got two possibilities:

sin x = 0.5
sin x = 0

From the second equation:

I got 0 and 180, or, in other words, 0 and 3.14. The book has these two answers but the only other answer it has is 6.28 (and by the way, my domain is 0 <= x <= 2π)

I tried in my calculator and the other answers I got seem to work: 30 degrees and 150 degrees but then, so does 6.28 which I am assuming the book got by adding 2π to the answer 0 from the second equation...

What am I doing wrong. Is the book missing my answers?

I'm also having problems with another question. I get some answers like the book but the others I get different too... I hope I am not the one wrong because I thought I was doing this right tan2x + 4tan x = 0

tan x = 0, outputting 0 and 3.14 and 6.28 as the book has, but, they also get: 2.90 and 6.04

tan x = - 4

I get: 4.96 and 1.82

That first problem is going to have an infinite number of solutions, I see at least 4 in the range 0 to 2π. It's likely your books just isn't listing them all. There are 2 solutions before .5 radians and after 0. If you are trying this on your calculator, try graphing it out with a range of 0 to 2π, and the Y set to [-4,4,1]. If you zoom close enough to where the wave meets the zero, you will see that it cross 2 times at each intersection.

Could you show how you are coming up with these answers? Or is this a calculator assignment?

tiny-tim
Homework Helper
Hi Peter! 2sin2x - sin x = 0

I got 0 and 180, or, in other words, 0 and 3.14. The book has these two answers but the only other answer it has is 6.28 (and by the way, my domain is 0 <= x <= 2π)
tan2x + 4tan x = 0

tan x = 0, outputting 0 and 3.14 and 6.28 as the book has, but, they also get: 2.90 and 6.04

tan x = - 4

I get: 4.96 and 1.82

Your book is rubbish. (which book is it?)

It looks as if the questions should be sin2x - 2sin x = 0 and 4tan2x + tan x = 0, in which case the answers given would be correct. (in the first one, your 6.28 is 2π, and that is in the domain, so you should have included it)

Ok, for the first question:

2sin2x - sin x = 0 for the range: 0 <= x <= 2π

First, I factorized: sin x (2 sin x - 1) = 0

Therefore, either: sin x = 0 (equation 1)
or: 2 sin x - 1 = 0, x = sin-1(0.5) (equation 2)

You see 4 answers there, I think I see five but I might be mistaken. The book finds only three: 0, 3.14 and 6.28

Well, continuing for equation 1: x = sin-1 (0) = 0. This was my first answer. Adding 360 (2π) still makes it fit in the range, so, I already have 2 answers.

But sin-1 (0) can also be equal to 180 degrees, not only 0, hence, another answer would be 180 degrees = π

Then I tried for equation 2:
x = sin-1(0.5)
= 30 degrees = π / 6

But sin of 150 also equals 0.5. Hence, we get another answer: 150 degrees = 5π/6

So I would actually have five answers:

0, π, 2π, π/6 and 5π/6

Last edited:
Hi Tiny-Tim,

Yes, the book is frustrating. I missed some lessons because of a school trip and I am trying to catch up by teaching myself and having a book with wrong answers is painful! (Good that I have the forum to resort to! )

The book is: Mathematics Standard Level for the IB Diploma (2004 Curriculum) by Smedley and Wiseman