Finding roots of a trigonometric equation
Maths and statistics discussion, revision, exam and homework help.
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Finding roots of a trigonometric equationA 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?
Please help.
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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.
Your working's fine, but think about whatWon't change to , to give another two roots?
Please help.
corresponds to, in the question given.
Dividing by zero is bad.
So we discard that solution. 
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Re: Finding roots of a trigonometric equationNeither sinx or cosx can equal zero because it is not permissible to divide by zero(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?
Please help.
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Re: Finding roots of a trigonometric equationNot 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.(Original post by Zishi)
Ahh, I thought that I could always rely on the answers found from calculations. Anyway, thanks to both of you.
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.
