Sine and Cosine Functions

The Unit Circle is used for 0, 90, 180, 270, and 360 degrees.

-Which is 0 degrees, pi/2, pi, 3pi/2, and 2pi in radians.

The angle tells you which point to use in the 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

Example 1:
Find the value of each expression.

*sin180 degrees= y/r =0/1 =0
sin180 degrees=0
--At 180, y is 0 and your radius is always 1.

*cos180 degrees= x/r = -1/1 =-1
cos180 degrees=-1
--At 180, x is -1 and your radius is always 1.

Example 2:
Find the value of each expression.

*sin(-pi)= y/r =0/1 =0
sin(-pi)=0
--At pi, which is 180 degrees, y is 0 and your radius is always 1.

*cos(pi/2)= x/r =0/1 =0
cos(pi/2)=0
--At pi/2, which is 90 degrees, x is 0 and your radius is always 1.

Example 3:
State whether each expression is positive, negative, or zero.

*cos89
--89 is in the first quadrant on the unit circle, and in the first quadrant, cos is positive.
--positive/1=positive
cos89=positive

*sin7pi/4
--multiple 7(180)/4, which gives you 315 degrees.
--315 is in the fourth quadrant on the unit circle, and in the fourth quadrant, sin is negative.
--negative/1=negative
sin7pi/4=negative