SOLUTION: A diagram is needed please i need to understand this .I am having a hard time. 1.)If P(-5/13,12/13) is on the point on the unit circle corresponding to the real number t, determ

Algebra ->  Trigonometry-basics -> SOLUTION: A diagram is needed please i need to understand this .I am having a hard time. 1.)If P(-5/13,12/13) is on the point on the unit circle corresponding to the real number t, determ      Log On


   

Question 756882: A diagram is needed please i need to understand this .I am having a hard time.
1.)If P(-5/13,12/13) is on the point on the unit circle corresponding to the real number t, determine the coordinates of
i)P(t-3pie)
ii)P(-t+pie)



2.)If P(t)=(7/25,24/25) be the point on the unit circle that corresponds to t.
Find P(t-pie).Is it -7/25,24/25?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Angle AOP, swept counterclockwise from OA to OP corresponds to t
Maybe t is the measure of AOP, or the measure of AOP plus a number of whole turns.
An angle measuring 2pi would be one whole counterclockwise turn.
An angle measuring pi would be half of a counterclockwise turn.
An angle measuring -pi would be half of a clockwise turn.

i. Adding or subtracting pi to angle t would take you to point Q, halfway across the circle.
P%28t-pi%29=Q%285%2F13%2C-12%2F13%29
Adding or subtracting 2pi would take you a full turn back to the same spot.
P%28t-3pi%29=P%28t-pi-2pi%29=P%28t-pi%29=highlight%28Q%285%2F13%2C-12%2F13%29%29

ii. A minus sign as in -t means go in the opposite direction, so P%28-t%29=B%28-5%2F13%2C-12%2F13%29.
Then, adding pi would take you halfway around the circle to
highlight%28P%28-t%2Bpi%29=C%285%2F13%2C12%2F13%29%29

2. If P(t)=(7/25,24/25), P(t-pi) is halfway across the circle at a point X
highlight%28P%28t-pi%29=X%28-7%2F25%2C-24%2F25%29%29