The Unit Circle

Hi, my name is Erika Madrid.

In class today, we reviewed about the C.A.S.T rule, the four quadrants and "Soh Cah Toa."

Equation: x^2 + y^2 = 1 or cos^2 θ + sin^2 θ= 1

REMEMBER: Positive distance is measured in counterclockwise direction; negative distance is measured in a clockwise direction.

Example: If ( x, 9/41) is a point on the unit circle in quadrant III, find the value of x and tan θ.

sin θ = 9/41 ( you use sin θ because it's 9/41 is on the II quadrant (s))

sin^2 θ + cos^2 θ = 1

(9/41)^2 + cos^2 θ = 1

cos^2 θ = 1 - (9/41)^2

cos^2 θ = 1 - 81/1684

cos θ = +- |1600/1681

cos θ = - 40/41

Then! You solve for tan θ.

tan θ= sinθ / cosθ

tan θ= (9/41)/ (-40/41)

tan θ= 9/41 - -41/40 = 369/1640

tan θ= -9/40

homework: NONE! :D