1. More Practice with Trigonometry Section 4.3b

2. Let’s consider… Quadrantal Angle – angles whose terminal sides lie along one of the coordinate axes Note: Quadrantal angles do not produce reference triangles, but we can still evaluate their trig. functions P(0,1)

3. More to consider… Quadrantal Angle – angles whose terminal sides lie along one of the coordinate axes Note: Quadrantal angles do not produce reference triangles, but we can still evaluate their trig. functions P(–1,0)

4. Still more to consider… Quadrantal Angle – angles whose terminal sides lie along one of the coordinate axes Note: Quadrantal angles do not produce reference triangles, but we can still evaluate their trig. functions P(0,–1) Undefined!!!

5. Trigonometric Functions of Real Numbers Unit Circle – a circle with radius 1 centered at the origin Wrapping Function – associates points on the number line with points on the unit circle P(x,y) (1,0) t t > 0 t t When the line is “wrapped around” the unit circle, each point t will fall on a point of the circle that lies on the terminal side of an angle t radians in standard position. This allows for an even nicer definition for trig functions…

6. Trigonometric Functions of Real Numbers Let t be any real number, and let P(x, y) be the point corresponding to t when the number line is wrapped onto the unit circle. Then t t

7. Let t be any real number, and let P(x, y) be the point corresponding to t when the number line is wrapped onto the unit circle. Then t t Note: The number t on the number line always wraps onto the point (cos t, sin t) on the unit circle!!! For this reason, the trig functions when applied to real numbers are usually called the circular functions.

8. Guided Practice Find and by using the given information to construct a reference triangle. 1.and With sin > 0, we’re in either QI or QII With tan < 0, we have QII Draw a reference triangle, with r = 7 and y = 3: 3 7 Use Pythag. Thm:

9. Guided Practice Find and by using the given information to construct a reference triangle. 1.and 3 7 Our Definitions:

10. Whiteboard Problems Find and by using the given information to construct a reference triangle. 2.and With sec > 0, we’re in either QI or QIV With sin > 0, we have QI 1 3 Our Definitions:

11. Whiteboard Problems Find and by using the given information to construct a reference triangle. 3.is und. and With cot und., we have y = 0 With sec < 0, terminal side is on neg. x-axis 1 Our Definitions:

12. Whiteboard Problems