1. TRIGONOMETRY: REVIEW SOHCAHTOA  Show that tan Ө=sin Ө/cosӨ Pythagoras a 2 +b 2 =c 2  Show that cos 2 Ө+sin 2 Ө=1 (÷c & substitute with trig ratios) π radians =180° Non-right Angles: When would you use the following? Ө O A H

2. SOH CAH TOA Sin=0/H --  O=H Sinx Applet: http://www.ies.co.jp/math/products/trig/applets/sixtrigfn/sixtrigfn.html http://www.ies.co.jp/math/products/trig/applets/sixtrigfn/sixtrigfn.html

3. Sketch the 3 trig functions

4. Sine Graph y=sinx Amplitude=1 Period=360 or 2 π Amplitude: Period: Frequency:

5. Cosine graph Amplitude: Period: Frequency:

6. Tangent graph Amplitude: Period: Frequency:

7. y=±A sinB(x±C) ± D

8. Reflects in the x axis -sinx-cosx-tanx

9. asinxacosxatanx Changes the amplitude (max distance from resting) of the graph y=2sinx y= cosx

10. sinbxcosbxtanbx Changes the frequency (how often it repeats in 2 π ) & period (horizontal distance for one cycle) y=sin3xfrequency x3, period ÷3 y=cos1/2 xfrequency ½ ed, period x2

11. sin(x-c) cos(x-c) tan (x-c) Moves graph sideways ( + left - right ) y=sin(x-45) y=cos(x+90)

12. sin(x)+d cos(x)+d tan(x)+d Moves graph up or down (+ up - down ) y=sin(x)+2 y=cos(x)-1

13. On Graphics Calculator eg: sketch f(x)=3sin2(x- π /4) Make sure you are in the right mode (rad/degrees) Enter equation (use brackets around inner function) Adjust view window: ◦ Think about the domain you want to see: one cycle/ 2 π (consider frequency & horizontal shift) ◦ Think about the range (consider amplitude change & vertical shift) ◦ If in radians, set the step as something including π (often π /2) Remember you can g-solve for points/use table function to plot.