The Unit Circle Dr Shildneck The Unit Circle

The Unit Circle Dr. Shildneck

The Unit Circle • The Unit Circle is a circle of radius 1 -unit. • Since angles have the same measure regardless of the size of their terminal side, we generally speak about their trigonometric ratios by using angles as they rotate around a unit circle.

Special Angles 120 o 90 o 60 o 135 o 45 o 150 o 30 o 180 o 0 o 360 o 330 o 210 o 225 o 315 o 240 o 270 o 300 o

Special Right Triangles x 2 30 – 60 – 90 1 2 x x = 45 – 90 1 1

Trig Values on the Unit Circle 150 o 30 o 1 1 30 o 1 210 o 30 o 1 330 o

Trig Values on the Unit Circle 45 o 1 45 o

Trig Values on the Unit Circle 135 o 45 o 1 1 225 o 1 45 o 45 o 1 315 o

Trig Values on the Unit Circle 60 o 1 60 o

Trig Values on the Unit Circle 120 o 60 o 1 60 o 60 o 1 240 o 1 1 300 o

SINE VALUES 90 120 60 45 135 30 150 180 0 360 330 210 225 315 240 300 270 0

COSINE VALUES 90 120 60 45 135 30 150 180 0 360 330 210 225 315 240 300 270 0

Completing the Unit Circle • Know the patterns for 45’s • Know the patterns for 60’s • Know the SIGNS (cosine – x, sine – y)

Completing the Table • Know the Unit Circle (sines and cosines) • Find Tangent (y/x = sine/cosine) • Know Reciprocals

Assignment 1) Complete Unit Circle 2) Complete Table Practice more than once Downloadable on Website