OCR C4 Parametric Equations Watch
1) A curve has the parametric equations 'x= asin g' 'y= agcos g'
Where a is a positive constant and range is between (and including) pi to negative pi.
i) Write down the value of g corresponding to the origin, and state the points A and B (y and x intercept respectively of the curve).
ii) Show that dy/dx = -1gtan g and hence find the equation of the tangent to the curve at the origin.
I know how to do part ii) with the right information I just thought I should put it in for context, any help would be great cheers
at A x=0 so asing = 0 so g = 0 (y = 0) or g= pi (y=-pi) or g = -pi (y = pi)
at B y=0 so agcosg = 0 so g=0 (x=0) or g=pi/2 (x=pi) or g=-pi/2 (x = pi/2)
so A = (0,0) or (0,-pi) or (0,pi)
and B=(pi/2,0) or (0,0)
(from the diagram it should be obvious which one is B and which is A)
dy/dx = (dy/dg) / (dg/dy) (chain rule)
= (-agsing + acosg)/ acosg = -gtang + 1 (product rule on agcosg)
at origin g = 0 so dy/dx = 1