The 3 Great Trigonometric

Properties

Draw 50O in Standard Position

X

Y

50Oyr

x

P(x,y)

Consider the SIN ratio (y/r). Where else on the circle could the point be?

X

Y

50Oyr

P(x,y)

The point could reflect in the y axis

X

Y

50Oyry r

P(x,y)P(x,y)

The point could reflect in the y axis

X

Y

50O

y r O2 = 130O

180O

P(x,y)

The Property of SINES

When sinO = k, two values of O that satisfy the equation are O, and 180O - O

Try SIN 30O and SIN 150O on your calculator…

Draw 50O in Standard Position

X

Y

50O

P(x,y)

Consider the COS ratio (x/r). Where else on the circle could the point be?

X

Y

50O

x

r

P(x,y)

The point could reflect in the x axis

X

Y

50O

x

r

r

P(x,y)

P(x,y)

The point could reflect in the x axis

X

Y

50O

50O

r

r

310O

360O P(x,y)

P(x,y)

The Property of COSINES

When cosO = k, two values of O that satisfy the equation are O, and 360O - O

Try COS 50O and COS 310O on your calculator …

Draw 50O in Standard Position

X

Y

50O

P(x,y)

Consider the TAN ratio (y/x). Where else on the circle could the point be?

X

Y

50Oy

x

P(x,y)

The point could reflect through the origin

X

Y

50O

- y- x

230O

50Oy

x

P(x,y)

P(x,y)

The Property of TANGENTS

When tanO = k, two values of O that satisfy the equation are O, and 180O + O

Try TAN 50O and TAN 230O on your calculator …

Find O for the following:

SINO = 0.55O = 33.4O or 146.6O

COSO = 0.95O = 18.2O or 341.8O

Given the point, find O and r

r

x

(5,7)

7

5O

yTANO = 7

5

O = 54.5O

r2 = 72 + 52

r = 8.6

Page 2781 (pg 259 #14)

[5,6] odd12,13,17,20