Its equation is:

*x*

^{2}+

*y*

^{2}= 1.

Its equation is also: x = cos(theta), y = sin(theta).

HOMEWORK part one: PROVE to yourself that

*x*

^{2}+

*y*

^{2}= 1

for every point in the following diagram.

For example,

(1,0) ==> x = 1 and y = 0 ==>

x^2 = 1 and y^2 = 0 ==> 1 + 0 = 1 check

x^2 = 1 and y^2 = 0 ==> 1 + 0 = 1 check

(√3/2, 1/2) ==> x = √3/2 and y = 1/2 ==>

x^2 = 3/4 and y^2 = 1/4 ==> 3/4 + 1/4 = 1 check

x^2 = 3/4 and y^2 = 1/4 ==> 3/4 + 1/4 = 1 check

(√2/2, √2/2) ==> x = √2/2 and y = √2/2 ==>

x^2 = 2/4 and y^2 = 2/4 ==> 2/4 + 2/4 = 1 check

x^2 = 2/4 and y^2 = 2/4 ==> 2/4 + 2/4 = 1 check

and so on for all the points around the circle.

HOMEWORK part two: PLAY with the following applets for the sin(theta) http://www.ies.co.jp/math/java/trig/graphSinX/graphSinX.html

and cos(theta) http://www.ies.co.jp/math/java/trig/graphCosX/graphCosX.html

and PROVE that sin(theta) = y and cos(theta) = x, for all the points

in the unit circle. Note, Don't forget to rotate the cos(theta) applet

after you have drawn it !