Finding t in the Two Tangent Lines at (0,2)

[razored]

Homework Statement [/b]
My book talks about find the two tangent lines at the point (0,2) for http://mathbin.net/equations/7402_0.png and http://mathbin.net/equations/7402_1.png .[/URL] It says that t then is equal to pi/2 and -pi/2. I do not know how to they solved for this t. Any help?

 

[CompuChip]

You solve the simultaneous equation
$$x = 0, y = 2$$

It's easiest starting with the latter:
$$2 = y = 2 - \pi \cos t \implies 0 = - \pi \cos t \implies t = \pm \frac{\pi}{2}$$
and then all you have to do is plug them both into the equation for x and check that it gives zero (i.e. you have two values of t for which (0, 2) is on the curve).

 

[razored]

Why didn't we include $$\frac{ \pi }{2}+2n \pi$$?

Thank you!

 

[CompuChip]

Because there are no such points at which the curve goes through (0, 2).
You can plug it in:
x(pi/2 + 2 pi) = ... ?