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5.5 Circular Functions: Graphs and Properties Tues Jan 14

5.5 Circular Functions: Graphs and Properties Tues Jan 14. Do Now Evaluate 1) Sin pi/2 2) Cos 2pi 3) Tan pi/4. Quiz Review. Retakes by next Wed. Circular Functions. The domains of the trigonometric functions have been sets of angles or rotations.

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5.5 Circular Functions: Graphs and Properties Tues Jan 14

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  1. 5.5 Circular Functions: Graphs and PropertiesTues Jan 14 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,

  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 #1-47 odds

  18. 5.5 Sine and Cosine Graph ReviewWed Jan 15 • 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? • SGO quiz tomorrow

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