1. 5.5 Circular Functions: Graphs and Properties Mon Nov 10 Do Now Evaluate 1) Sin pi/2 2) Cos 2pi 3) Tan pi/4

2. Quiz Review Retakes by next Wed

3. Circular Functions The domains of the trigonometric functions have been sets of angles or rotations. Trigonometric functions with domains composed of real numbers (radians) are called circular functions

4. Basic Circular Functions With respect to S radians and the unit circle,

5. Reflections on the Unit Circle Because the unit circle is symmetric, we can use the coordinates of one point on the unit circle to find coordinates of its reflections (Draw unit circle with point x,y )

6. Ex1 The point (3/5, 4/5) lies on the unit circle. Find its reflections across the x-axis, y-axis, and origin

7. Finding Function Values Knowing the coordinates of only a few points on the unit circle + reflections allows you to find many trig values

8. Ex Find each of the following using reflections 1) 2) 3)

9. Calculator and Radians When working in radians, make sure the calculator is set to radians mode! MODE -> RADIANS should be highlighted

10. Graphs of Sine and Cosine Functions One characteristic about circular functions is that they repeat, or oscillate Since circular functions travel on a circle, they tend to repeat every revolution

11. Graph of y = sin x Let’s look at the y-coordinate on the unit circle

12. Graph of y = cos x Let’s look at the x-coordinate of the unit circle

13. Domain and Range The domain and range of both sine and cosine functions are the same Domain = All real numbers Range = [-1, 1]

14. Period of sine and cosine A function with a repeating pattern is called periodic. All trig graphs are periodic. The period of y = sin x and y = cos x is 2pi

15. Amplitude The amplitude of a periodic function is defined as one half of the distance between its maximum and minimum values You can calculate this by dividing the range by 2 The amplitude of y = sin x and y = cos x is 1

16. Symmetry Sin (-x) = - sin x The sine function is odd Cos (-x) = cos x The cosine function is even

17. Closure Describe the graphs of the sine and cosine functions. How are they similar? Different? HW: p.505 #1-43 odds

18. 5.5 Sine and Cosine Graph Review Tues Nov 11 Do Now Evaluate 1) 2)

19. HW Review: p.505 #1-47

20. Review of Sine and Cosine Graph

21. (If time) The other 4 trig graphs Tan x and cot x These 2 graphs have asymptotes

22. Sec x and csc x These 2 also have asymptotes

23. Closure Why are the other 4 trig graphs different than sine and cosine?