http://prntscr.com/ayxs6p I do NOT get why I got the last part wrong?!

Question

noobsteriscastic · Answer

How did you find it?

kikuo · Answer

What subject is this specifically? 
(Just curious can't help)

noobsteriscastic · Answer

ok i have an idea. you do know that the object is going to be at the same point (0,1) after one revolution? So how about you use these coordinates in parametric equations and find t.
In simpler words, use (x,y)=(0,1) in given equations to find t. You'll find two values of t. One will be zero (because the object was at (0,1) at t=0 too). The other one is your solution. 
Did i make any sense?

kittiwitti1 · Answer

This is an example, but that's my work as well... http://prntscr.com/ayxuqa Mathematics 180 @Kikuo

kittiwitti1 · Answer

Yeah, I get it @Noobsteriscastic but it says $2\pi$ is wrong D:

kittiwitti1 · Answer

I mean $\frac{\pi}{2}$

noobsteriscastic · Answer

That's because 2pi is wrong. What are the solutions of these:$$\sin (8t)=0 and \cos(8t)=1$$

kittiwitti1 · Answer

Well, whatever the answer is, it's not $\pi$,$2\pi$, or $\frac{\pi}{2}$ ; - ;

kittiwitti1 · Answer

I meant pi/2 when I typed 2pi sorry

noobsteriscastic · Answer

Period of both sine and cosine are 2pi. Look at the argument of sine and cosine here, it's 8t not just t. 
So one period is equivalent to:
8t=2pi
t=pi/4

kittiwitti1 · Answer

Oh... I see.

I can't believe I missed that e_o
Thank you for pointing it out!

noobsteriscastic · Answer

well you got it! Cheers