Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P.
$\displaystyle (a)2\pi$ $\displaystyle (b)-3\pi$
Can someone please help me I dont know what is it that I need to do find the coordinates?
Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P.
$\displaystyle (a)2\pi$ $\displaystyle (b)-3\pi$
Can someone please help me I dont know what is it that I need to do find the coordinates?
Using skeeter's neat diagram,
you need to locate the angles $\displaystyle t=2\pi$
and $\displaystyle t=-3\pi$
$\displaystyle 2\pi$ corresponds to zero degrees on the extreme right on the x-axis where the circle touches the axis.
The co-ordinates are (1,0).
You can also obtain these by calculating $\displaystyle Cos(2\pi)$ and $\displaystyle Sin(2\pi)$
The angle $\displaystyle t=-3\pi$ is a negative angle.
Positive angles are anticlockwise.
Negative angles are clockwise.
Angles start from zero or $\displaystyle 2\pi$.
$\displaystyle -3\pi$ means go $\displaystyle 2\pi$ radians clockwise, then another $\displaystyle \pi$ radians clockwise.
This causes us to end up at $\displaystyle \pi$ radians.
You can read off the co-ordinates of this position on the circle,
or you can use your calculator to calculate $\displaystyle Cos(-3\pi)$ for the x co-ordinate, and $\displaystyle Sin(-3\pi)$ for the y co-ordinate.
Why not try this and check that the co-ordinates calculated match skeeter's diagram.
Remember... x=Cos(angle), y=Sin(angle) on the unit circle.
There must be more to the question...
For (a) the point (1,0) are the co-ordinates of zero or $\displaystyle 2\pi$
(0,1) are the co-ordinates of $\displaystyle \frac{\pi}{2}$
(-1,0) are the co-ordinates of $\displaystyle \pi$
(0,-1) are the co-ordinates of $\displaystyle \frac{3\pi}{2}$
Check your book again for the entire question.