 Revolutions Around the Unit Circle  We can revolve around the unit circle in the and directions.   Revolution in the positive direction is.   Revolution in the negative direction is. positivenegative counterclockwise clockwise

 With the unit circle, the x and y coordinates are dependent upon the real number, θ, which represents the location in degrees or radians of a point in the unit circle. With this knowledge, let us define the Sine and Cosine function.  Let be a real number in degrees or radians, and (x, y ) be the corresponding point on the unit circle.  So, the coordinates of a point on the unit circle can also be defined as.

a.b. c.d.

 In which quadrant(s) is cosine positive?  In which quadrant(s) is sine positive?

 Let θ be a real number and ( x,y ) be the corresponding point on the unit circle. furthermore,

 a.b.  c.d.

 Which quadrant(s) is the tangent function positive?

 a.b.  c.d.

There are actually three more trigonometric functions that we haven’t yet defined: Cosecant, Secant, and Cotangent. They are all functions of the three we already know! reciprocal

5.

6.

7.8.

9.10.

11.12.

 13. In which two quadrants is cosecant negative?  14. When is secant undefined?

RadianDegree