The unit circle

The unit circle

In today's class we learned about unit circles. Unit circle is a circle with its centre at the origin and with a radius of one unit.

The equation for unit circle is: x squared+ y squared= one
A few class's ago we learned that positive distance is measured in a counter clock wise of a circle,and negative distance is measured in a clockwise of a circle.

we learned that the notation p(theta) is used to denote the terminal point,where the terminal arm of angle theta intercepts the unit circle, for every arc length theta on the unit circle, p(theta) is unique.
we can define p(theta) as the ordered pair p(x,y)

we were also reminded of SOH, CAH, TOA and what they stand for:

sin(theta)=opposite over hypotenuse

cos(theta)=adjacent over hypotenuse

tan(theta)=opposite over adjacent

using SOH ,CAH ,TOA we can found the p(theta) of an angle like we did in class,we found that:

sin(theta)=Y over 1 which sin(theta) equals Y

cos(theta)=X over 1 which cos(theta)equals X

tan(theta)=y over X

All that means is that the y axis is sin(theta) and x axis is cos(theta). Therefore, p(x,y)=p(cosO,sinO),and since the equation for unit circle is x squared+ y squared= one, it would be cos(squared) theta +sin(squared)theta=one.

And we were also reminded of the four quadrant and the rule of CAST.

quadrant 1 A quadrant 2 S quadrant 3 T quadrant 4 C


sin(theta) is + sin(theta) is + sin(theta) is _ sin(theta) is _

cos(theta) is + cos(theta) is _ cos(theta) is _ cos(theta) is +

tan(theta) is + tan(theta) is _ tan(theta) is + tan(theta) is _

Now one example of what we learned today is: where does p(theta) lie, given 0<2pi>