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Trigonometry: Review

Trigonometry: Review. SOHCAHTOA Show that tan Ө =sin Ө / cos Ө 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?. H. O. Ө. A. SOH CAH TOA. Sin=0/H -- O=H Sinx.

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Trigonometry: Review

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  1. Trigonometry: Review • SOHCAHTOA • Show that tanӨ=sinӨ/cosӨ • Pythagoras a2+b2=c2 • Show that cos2 Ө+sin2Ө=1 (÷c & substitute with trig ratios) • πradians =180° • Non-right Angles: When would you use the following? H O Ө A

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

  3. Sketch the 3 trig functions

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

  5. Cosine graph Amplitude: Period: Frequency:

  6. Tangent graph Amplitude: Period: Frequency:

  7. y=±A sinB(x±C) ± D

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

  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 2π) &period (horizontal distance for one cycle) • y=sin3x frequency x3 , period ÷3 • y=cos1/2 x frequency 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)+dcos(x)+d tan(x)+d • Moves graph up or down (+ up - down ) • y=sin(x)+2 • y=cos(x)-1

  13. On Graphics Calculatoreg: 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/ 2π (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.

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