The parametric equations of a curve are x=2cos t
and y=2sin t, for 0

Question

The parametric equations of a curve are x=2cos t
and y=2sin t, for 0 <= t <2 pi.
What is the value of t at the point (0,2)?

anonymous · Answer

$$x=2\cos ~t$$$$y=2\sin~t$$
$$0 \le t < \pi$$

.sam. · Answer

You taking A levels?

anonymous · Answer

Yes. How did you know?

.sam. · Answer

got the feel of it

.sam. · Answer

ok, so just differentiate x and y

.sam. · Answer

x=2cost
dx/dt=-2sint
--------------------
y=2sint
dy/dt=2cost

.sam. · Answer

then $$\frac{dy}{dx}=\frac{2cost}{-2sint}$$
$$\frac{dy}{dx}=-\cot~t$$

.sam. · Answer

$$y-y_1=m(x-x_1)$$
$$y-2=-\cot~t(x-0)$$
$$y=-xcot ~t +2$$

.sam. · Answer

Try Substitute (0,2) into x=2cos t and y=2sin t

.sam. · Answer

t should be pi/2

anonymous · Answer

Ok, that's the answer. but why?

anonymous · Answer

Oh, I know why. Thank you! :D

.sam. · Answer

Because x=2cos t and y=2sin t is a part of the curve, and y=−xcot t+2 also part of a curve, So, substitute (0,2) into both equation will get the same value