This document discusses trigonometric ratios and the unit circle. It introduces the CAST rule for determining the quadrant of a point based on the signs of trig functions. It explains how to find the corresponding point on the unit circle given coordinates or trig function values. Finally, it introduces cosecant, secant, and cotangent as reciprocal trig functions and gives an example of finding multiple trig ratios given a sine value.

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