Trigonometry

Trigonometry

1. Basic Definitions

   • sinx=o/h
   • cosx= a/h
   • tanx= o/a
     • tan=sinx/cosx
   • cotx= 1/tanx
   • secx= 1/cosx
     • sec^2x= 1+tan^2x
   • cosecx=1/sinx
     • cot^2x +1= csc^2x

2. Complementary Angles

   • Sum= 90 degrees
     • ie. 30dg and 60dg

3. Exact Values

   • Degrees and Radians
     • ie. 360dg= 2pi
       • 1rad= 180/pi

4. Rules of Signs

   • cast diagram
     • ie. sinx>0 = 1st and 2nd quad

5. Pythagoras' Theorem

   • x^2+y^2=r^2
     • x^2/r^2+y^2/r^2=1
       • cos^2x + sin^2x= 1

6. Graphs

   • y= Asin(Bx+C)+D
     • A- Amplitude
     • B- Period (2pi/B)
     • C= Horizontal shift
     • Vertical shift

7. Compound Angles

   • sin(A+B)= sinAcosB + cosAsinB
   • cos(A+B)= cosAcosB-sinAsinB
   • tan(A+B)= tanA+tanB/1-tanAtanB

8. Double Angles

   • sin(2a)= 2sinacosa
   • cos(2a)= cos^2a-sin^2a
     • 2cos^2a-1
     • 1-2sin^2a

9. Product Formulae

   • SinAcosB=1/2[sin(A+B) + sin(A-B)]
   • CosAcosB=1/2[cos(A+B)+cos(A-B)]
   • sinAsinB=1/2[cos(a-b)-cos(a+b)]

10. Polar Coordinates

    • x=rcosx
    • y=rsinx
    • r= sqrt(x^2 + y^2)
    • Polar coordinates (r,θ)

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