1. Trig Ratios & Unit Circle
Using Pyth
On unit circle
This is true for
on the unit circle
Ex. Is the point (2, 1/2) on the unit circle?

2. Coordinates of Points on Unit Circle
cos
=x=x=x
=y=y=y
r 1
Conclusion: For all points on the unit circle, since
r = 1, we can replace cos with x and sin with y

3. ) represent any point on the unit circle
and has the coordinates (cos , sin )
SO, P( ) = (cos , sin )
How about, tan = y = sin
x cos

4. This is summarized in CAST rule
In which quadrant does the terminal arm of
a) sin < 0 and tan > 0
b) cos < 0 and tan < 0
lie if:

5. Finding P( ) on Unit Circle
If given a point with coordinates (5, 12),
how do you find the corresponding point
on the unit circle, ie, P( ) ?
If sin
=
Find tan
and
cos
=

6. If cos =
Given sin =
, find sin
and tan < 0, find cos.

7. 3 New Reciprocal Trig
Ratios or Functions
= sec =
1 = 1 = r
cos
x
x
r
cosecant = csc =
1 = 1 = r
sin
y
y
r
cotangent = cot = cos
CAST still applies
Give 6 trig ratios over (0, ) if sin = 3
5