This document discusses trigonometric ratios and the unit circle. It explains that for any point (x,y) on the unit circle, x=cosθ and y=sinθ. It also reviews trig ratio definitions and relationships like tangent=sin/cos. The document provides examples of finding trig function values given other information about a point on the unit circle. It introduces cosecant, secant and cotangent as reciprocal trig functions and confirms the CAST rule applies to them as well.

1. Trig Ratios & Unit Circle
Using Pyth
On unit circle
This is true for
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 lie if:
a) sin < 0 and tan > 0
b) cos < 0 and tan < 0

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 = and cos =
Find tan

6. If cos = , find sin
Given 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