And the question is: How do I solve trigonometric equations?Hope this helps!

[Peter G.]

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?

Thanks in advance!

 

[Peter G.]

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

 

[QuarkCharmer]

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]

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)

 

[Peter G.]

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

This far I already have three answers: 0, π and 2π

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

 

[Peter G.]

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