Solve this set of parametric equations in terms of t using just trig identities

How can I solve these set of parametric equations in terms of t using just trig identities?
x = tan t, y = sin t.

Thanks so much for your help!

Reply 1

mqb2766

Original post by Silverwolf146

How can I solve these set of parametric equations in terms of t using just trig identities?
x = tan t, y = sin t.
Thanks so much for your help!

You should know the basic trig identity/definition for tan ...

Reply 2

tonyiptony

Uh... what do you mean by solve? We have 2 equations and 3 unknowns - there is definitely not a unique solution.

If you want to eliminate t, well, what trig identities do you know? (Like seriously, write them all down, perhaps with reference to your notes - surely some will work)

(edited 1 month ago)

Reply 3

Expert Sandra

Original post by Silverwolf146

How can I solve these set of parametric equations in terms of t using just trig identities?
x = tan t, y = sin t.
Thanks so much for your help!

I can Help you handle this

Reply 4

thejohnwatson

To solve x=tan⁡tx = \tan tx=tant and y=sin⁡ty = \sin ty=sint, use the identity:
sin⁡2t+cos⁡2t=1\sin^2 t + \cos^2 t = 1sin2t+cos2t=1
Since tan⁡t=sin⁡tcos⁡t\tan t = \frac{\sin t}{\cos t}tant=costsint, solve for cos⁡t\cos tcost in terms of xxx:
x=ycos⁡t ⟹ cos⁡t=yxx = \frac{y}{\cos t} \implies \cos t = \frac{y}{x}x=costy⟹cost=xy
Substitute into the identity:
y2+(yx)2=1y^2 + \left(\frac{y}{x}\right)^2 = 1y2+(xy)2=1
This gives a relation between xxx and yyy

Reply 5

davros

Original post by thejohnwatson

Your post hasn't come out in a readable format, but please note for future reference that it's against forum rules to post full solutions to problems - please stick to hints, suggestions etc as per forum guidelines. Thanks.