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September 24, 2025, 08:21:27 pm
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Author Topic: Circular Function Equations  (Read 788 times)  Share 

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mandy

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Circular Function Equations
« on: March 28, 2010, 11:14:21 pm »
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Find the minimum positive value of so that the equation = will have no solution over the domain .

This is what I've done so far, I have no idea if it's right:
=


So then for the equation to have no solution, the angle has to be or .
But what do I do now?
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the.watchman

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Re: Circular Function Equations
« Reply #1 on: March 28, 2010, 11:18:39 pm »
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There must be no solution for , so try
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mandy

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Re: Circular Function Equations
« Reply #2 on: March 28, 2010, 11:23:26 pm »
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Quote from: the.watchman on March 28, 2010, 11:18:39 pm
There must be no solution for , so try

Sorry, what? I still don't know what to do now :(
« Last Edit: March 28, 2010, 11:37:43 pm by mandy »
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qshyrn

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Re: Circular Function Equations
« Reply #3 on: March 29, 2010, 01:51:41 am »
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from tan (4pi.x)=k
4pix is in 1st quadrant
if k is less than 0, then it wont have any solution (tan is positive in first quadrant remember)
dunno if this is right or not
« Last Edit: March 29, 2010, 02:11:39 pm by qshyrn »
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kyzoo

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Re: Circular Function Equations
« Reply #4 on: March 29, 2010, 03:14:14 am »
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Because the domain is [0, 0.1]

Therefore





---



So there is no solution to this equation when

Therefore the minimum positive value of k is
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mandy

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Re: Circular Function Equations
« Reply #5 on: March 29, 2010, 01:00:59 pm »
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Thanks guys, I understand now :)
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the.watchman

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Re: Circular Function Equations
« Reply #6 on: March 29, 2010, 01:04:20 pm »
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Quote from: mandy on March 29, 2010, 01:00:59 pm
Thanks guys, I understand now :)

Sorry I didn't see your reply to my post :)

Quote from: mandy on March 28, 2010, 11:23:26 pm
Quote from: the.watchman on March 28, 2010, 11:18:39 pm
There must be no solution for , so try

Sorry, what? I still don't know what to do now :(
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