Unit Circles ;);) ouuuweeee.

Last week one of our lessons were about Unit Circles.

The definition of a unit circle is that its used for 0 degrees, 90 degrees,180 degrees,270 degrees, and etc. Also 0, Pi/2, Pi,,3Pi/2,and 2Pi.

The angles tell you which point to use in formulas:

sin(theta)= y/r cos(theta)=x/r tan(theta)=y/x

csc(theta)=r/y sec(theta)=r/x cot(theta)=x/y

Ex.1 sin115(degrees) = y/r = pos.# / 1 = 1

b. cos(-3Pi/2)= x/r = neg. # / 1= -1

c.tan90(degrees)= y/x = 1/0 = undefined

d.sin400(degrees) = sin40 = y/r = 1/1 =1

400-360=40degrees

Ex.2 To clarify if degrees is positive or negative you have to sketch a drawing of the quadrants,then place a line through the quadrant with that degrees. If its the 1^st or 2^nd quadrant,it is always positive. If it is the 3^rd or 4th quadrant it is always negative.

a. sin225(degrees) would be placed within the III quadrant, because it falls between 180 and 270. Therefore it would be a negative number.

Sin= y/r = - #/1 = negative

b. cos345(degrees) would be placed in the IV quadrant,because it is between 270 and 360 degrees. Therefore this number would also be negative.

Cos= x/r = - #/1 = negative