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# Finding roots of a trigonometric equation Tweet

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1. Finding roots of a trigonometric equation
A question asks me to find the roots of the equation in the range 0o<x<360o. Here's how I tried to solve it:

I have been taught to not to cancel anything while solving trigonometric equation, so:

Taking sin x cos x common gives:

So, solving and should gives me the roots, but the wolfram alpha only gives the roots from as the answer.

Won't change to , to give another two roots?

2. Re: Finding roots of a trigonometric equation
(Original post by Zishi)
A question asks me to find the roots of the equation in the range 0o<x<360o. Here's how I tried to solve it:

I have been taught to not to cancel anything while solving trigonometric equation, so:

Taking sin x cos x common gives:

So, solving and should gives me the roots, but the wolfram alpha only gives the roots from as the answer.
Won't change to , to give another two roots?

Your working's fine, but think about what corresponds to, in the question given.

3. Re: Finding roots of a trigonometric equation
(Original post by Zishi)
A question asks me to find the roots of the equation in the range 0o<x<360o. Here's how I tried to solve it:

I have been taught to not to cancel anything while solving trigonometric equation, so:

Taking sin x cos x common gives:

So, solving and should gives me the roots, but the wolfram alpha only gives the roots from as the answer.

Won't change to , to give another two roots?

Neither sinx or cosx can equal zero because it is not permissible to divide by zero
4. Re: Finding roots of a trigonometric equation
Ahh, I thought that I could always rely on the answers found from calculations. Anyway, thanks to both of you.
5. Re: Finding roots of a trigonometric equation
(Original post by Zishi)
Ahh, I thought that I could always rely on the answers found from calculations. Anyway, thanks to both of you.
Not exactly. I'm sure you've done questions where you have constraints, and you'll find that one solution is not applicable considering the question you've done.

Silly example: Find the values of for , where . You'd say: Ahahah! I know that , but since the question tells me , then .

Since you received , you know this means either or or both.

But look at what the initial question said: .

That kind of already tells you that .

*You are being taught correctly in not to cancel anything at all (not just in trigonometric equations) - but what you need to know is to check what you have calculated to see if it makes sense with the initial conditions in the question.