Question

Question on a practice exam? Don't understand what they mean?

Answer 1

Which of the following particles is NOT moving along the unit circle in the xy-plane?

Select one:
a. A particle is moving in the xy-plane such that x=\cos (t+1), y=\sin (t+1) at time t.
b. A particle is moving in the xy-plane such that x=\cos t, y=\sin t at time t.
c. A particle is moving in the xy-plane such that x=\cos 5t, y=\sin 5t at time t.
d. A particle is moving in the xy-plane such that x=5\cos t, y=\sin t at time t.
e. A particle is moving in the xy-plane such that x=\sin t, y=\cos t at time t.

Ignore all the dashes. Sorry about that.

Answer 2

well, what is a unit circle?

Answer 3

these look like parametric parameters

recall that the unit circle has the equation: x^2 + y^2 = 1

Answer 4

the trig equivalent to that is just:

cos^2 (u) + sin^2 (u) = 1

Answer 5

So I would just have to find for whichever one that isn't true?

Answer 6

thats correct

Answer 7

If I have cos(t+1) + sin(t+1)= 1, how do I solve this?

Answer 8

let t+1 = u

cos^2 (u) + sin^2 (u)= 1 this is good, since it matches the
trig equivalent of x^2 + y^2 = 1

Answer 9

only one of these options is NOT like te others, can you pick it?

Answer 10

D?

Answer 11

if the xy innards are the same: t+1 ad t+1, just let them by u

x=\cos (t+1), y=\sin (t+1) at time t.
cosu sinu

x=\cos t, y=\sin t at time t.
cosu sinu

x=\cos 5t, y=\sin 5t at time t.
cosu sinu

x=5\cos t, y=\sin t at time t.
5 cosu sinu

x=\sin t, y=\cos t at time t.
sinu cosu

Answer 12

yeah, that 5 is going to wreck havok for the unit circle stuff

Answer 13

Okay, got it thank you : )

Answer 14

youre welcome