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You Are Here: Home > Answer Board > Algebra thru Pre-Calculus > Topic: CALCULUS WITH ANALYTIC GEOMETRY I-LINES AND CIRCLES
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CALCULUS WITH ANALYTIC GEOMETRY I-LINES AND CIRCLES

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Date Posted: 7/23/2008 11:11:46 PM  Status: Live
CALCULUS WITH ANALYTIC GEOMETRY I-LINES AND CIRCLES
Course Textbook Chapter Problem
Precalculus N/A N/A N/A
Question Details:
suppose that the perpendicular line ON from the origin O to the line L (the point N is on L) has a constant length of p units,and that ON makes a fixed angle θ with the positive x-axis.
Show that L is described by x cos(θ) + y sin(θ)=p
 
Please help asap....

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Date Posted: 7/24/2008 2:31:28 PM  Status: Live
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Response:
 
sinθ = y/p, so y=sinθ*p
 
cosθ=x/p, so x=cosθ*p
 
we know x2+ Y2 = P2
or x*x + y*y = p*p, or (x*x + y*y)/p= p
 replace x=cosθ*p and y=sinθ*p to the left side we have
(x*cosθ*p + y*sinθ*p)/p = p
or x cos(θ) + y sin(θ)=p
 
this equation is true for any point N that lies on L.
 
 

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Date Posted: 7/24/2008 9:03:50 PM  Status: Live
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Response:
This question belongs in the calculus section.
 
 
If you do not know how to answer questions posted or if you are unsure about how to reply, please move on to the next question(s).  A wrong reply will only add to my confusion.  Clear? 



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