# Thread: Trigonometric Functions of Real Numbers

1. ## Trigonometric Functions of Real Numbers

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?

2. Originally Posted by purplec16
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?
hi purplec16,

Cos(t) gives you the x co-ordinate of P
Sin(t) gives you the y co-ordinate of P

where t are the values given in (a) and (b)

3. i still dont really understand what to do

4. Originally Posted by purplec16
i still dont really understand what to do
you need to learn the unit circle ...

5. I mean I did but how will all of that come together to solve my problem?

6. 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.

7. So, in my math text, they have the answer for a and b as:
$\displaystyle (a) (1,0); (0,1); (0,U); (1,U)$
$\displaystyle (b) (-1,0);0,-1;0,U;-1,U$

How is it that they got those answers?

U: undefined

8. 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.

9. The questions states: Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometic functions of t, whenever possible.

(a) $\displaystyle 2\pi$ (b)$\displaystyle -3\pi$

10. Originally Posted by purplec16
So, in my math text, they have the answer for a and b as:
$\displaystyle (a) (1,0); (0,1); (0,U); (1,U)$
$\displaystyle (b) (-1,0);0,-1;0,U;-1,U$

How is it that they got those answers?

U: undefined
For (a) the first pair in brackets are the co-ordinates (x,y).
The second pair is (Sin(t), Cos(t))
The third pair is (Tan(t), Cot(t))
The fourth pair is (Sec(t), Cosec(t))

Same situation for (b) corresponding to $\displaystyle t=-3\pi$