Section 13.6a The Unit Circle

Positive angle of rotation The Unit Circle (like any circle) contains 360° It’s called the Unit Circle because the length of the radius is 1 π π/2 r = 1 Positive angle of rotation is counter clock-wise

((opposite)/(hypotenuse) The Unit Circle ((opposite)/(hypotenuse) 1 y (1, 0)  x (adjacent) / (hypotenuse)) Therefore, the coordinates of any point on the circle are: (cos , sin )

Values of the Unit Circle sin 30o = r = 1 30o cos 30o =

Values of the Unit Circle sin 45o = r = 1 45o cos 45o =

Values of the Unit Circle sin 60o = r = 1 60o cos 60o =

Values of the Unit Circle sin 135o = cos 135o =

- - - - Signs of Trigonometric Functions + + + A S Quadrant + + + Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj + + + A S Quadrant + + + - - - I - All + - II - Sin T C III - Tan IV - Cos All Students Take Calculus

1.) using the unit circle convert each measure from degrees to radians a) 150° b) 225° c) 480° 2.) using the unit circle convert each measure from radians to degrees a) b) c)

3.) use the unit circle to find the exact value of each a) sin 120° b) tan 225° 4.) use the unit circle to find sine, cosine and tangent of each a) b)

Homework Worksheet 13-3B