## anonymous one year ago If x=cost and y=tant, how do I get rid of the parameter?

1. welshfella

if y is the tangent of t then t is the angle whose tangent is y so we can write t = tan-1 y or t = arctan y do a similar procedure with y = cos t then you can form a relation between x and y

2. Kainui

I'd do it this way: $y=\tan t = \frac{ \sin t}{\cos t}$ Now we know we can plug in $$\cos t =x$$ but what about the $$\sin t$$ part? Well here's a trick, use the Pythagorean identity: $\sin^2 t + \cos^2 t = 1$ We can rearrange to get: $\sin t = \sqrt{1- x^2}$ So now we can finish plugging in: $y= \frac{ \sin t}{\cos t} = \frac{\sqrt{1-x^2}}{x}$

3. anonymous

is + or - not necessary here? for the Square Root

4. welshfella

I think not because the angles are considered to be only in the first quadrant

5. Kainui

Oh yeah I think $$\pm$$ is a good idea @ArkGoLucky

6. anonymous

Oh okay. Thanks.

7. anonymous

Could you help me with one more problem while you are here?

8. anonymous

Well either of you