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Topic: looking for a trig proof
Replies: 4   Last Post: Mar 23, 2017 9:23 AM

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 Wally W. Posts: 283 Registered: 6/15/11
Re: looking for a trig proof
Posted: Mar 23, 2017 8:52 AM

On Wed, 22 Mar 2017 22:54:12 -0700, William Elliot wrote:

>On Wed, 22 Mar 2017, James Waldby wrote:
>

>> On Wed, 22 Mar 2017 09:55:22 +0000, Popping mad wrote:
>>

>> > A = x cos? + y sin?
>> >
>> > Has anyone seen the proof for this
>> > for a line. I ran across it in the Hough Transform as a parameterized
>> > version for the definition of a line

>>
>> I don't know just what you mean by the "for a line" phrase,

>
>
>The equation of a line in the xy plane is
> ax + by = c.
>
>Dividing through by sqr(a^2 + b^2) gives the form
> x.sin t + y.cos t = d.

Which can be written as:

y = d / cos(t) - x * tan(t)

Why does parameterizing help?

>> but if, for example, your rho is the length of the hypotenuse
>> of a right triangle with horizontal side length x and vertical
>> side length y, then x = rho cos theta, y = rho sin theta,
>> whence x cos theta + y sin theta = rho cos^2 theta + rho sin^2 theta
>> which equals rho because cos^2 theta + sin^2 theta = 1.

>
>There was no rho in his equation.
>News groups are plain text only.
>Control characters don't show correctly to everybody.

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