Trigonometry

Trigonometry

1. Labeling the sides of a right triangle

   • Hypotenuse
     • Side directly opposite to the right angle in a right triangle
   • Adjacent
     • Side that forms the angle theta with the hypotenuse. The hypotenuse can't be the adjacent angle.
   • Opposite
     • Side directly opposite to theta and that doesn't contribute to it's formation.

2. The trigonometric ratios

   • Tangent (tan)
     •                         Opposite tan(theta) = -----------------                          Adjacent
   • Cosine (cos)
     •                            Adjacent Cos(theta) = --------------------                           Hypotenuse
   • Sine (sin)
     •                        Opposite Sin(theta) =  ---------------                        Hypotenuse
   • SOH CAH TOA
     • SOH: sin = opposite/hypotenuse CAH: cos = adjacent/hypotenuse TOA: tan = opposite/adjacent
   • Finding angles
     • If the ratio equation ends up similar to                         3 Sin(theta)= -----                                           2 then:                                             3 Theta = sin^-1 ( ---- )                                                      2
   • The unit circle
     • A circle with a radius of one unit that is devided into four quadrants. it is used to measure the sin and cos of various angles. [pic in book]

3. True Bearings

   • Clockwise measurements of angles by comparing them to true north direction (directly up). 
   • Tips
     • Do / use diagram (as accurate as possible and/or well labeled. Follow all inststructions Will most likely lead to SOHCAHTOA question Solve

4. 3D Problem Solving

   • generally involve pithagoras in 3d figures (cubes, etc) can be quite long and time consuming
   • Tips
     • read several times, can often cause epiphany look at diagrams caefully draw surfaces of figure if helpfull (can ask for spare paper)