Trigonometry Unit 2: 2-dimensional Motion From:

Why Trig? In physics, we can reduce all spatial problems into right triangle problems. Usually we can make problems “fit” into 1 of 2 situations. 1. Given a right triangle with known hypotenuse and on the the acute angles, find the two legs. 2. Given a triangle with known legs, find the hypotenuse and one of the acute angles.

Right Triangle Trig We will be using the three basic trig functions Sine – Opposite/Hypotenuse Cosine – Adjacent/Hypotenuse Tangent – Opposite/Adjacent

Basic Information The Hardest part of this process is determining what is opposite and what is adjacent. Make sure your calculator is in degree mode. It Defaults to radian mode, so always check before you start a problem.

The Side Opposite to  is a The Side Adjacent to  is b The Side Opposite to  is b The Side Adjacent to  is a No matter which acute angle you are dealing with, the hypotenuse is c a b c  

The ratios sin  = (a/c) cos  = (b/c) tan  = (a/b) sin  = (b/c) cos  = (a/c) tan  = (b/a) b c    a

Sample Problems: a = 4, b = 7, c = 10 Sin  = (4/10) = 0.4 Cos  = (4/10) = 0.4 sin  = (7/10) = 0.7 tan  = (4/7) = 0.57 b c   a

The Hypotenuse and an angle If you know the hypotenuse and one angle, you can determine the missing legs

The formulas Since cos  = (x/h) Then x = h(cos  ) Since sin  = (y/h) Then y = h(sin  ) b c  a (x) (y)

Sample Problems:  = & h= 75.1 Find x Cos  = (x/h) x = h cos  x = 75.1 (cos42.5) x = Find y sin  = (y/h) y = h sin  y = 75.1 (sin42.5) y = 50.7 b c  a (x) (y)

Reverse The trig functions can also be use to determine and angle when the sides are known. In order to do this, you must use the sin -1, cos -1, or tan -1. (The inverse functions) Use the second button on your calculator and then press SIN, COS, or TAN.

Sample Problem Find  if x = 17 and y = 12 Tan -1 (y/x) =  Tan -1 (12/17) =   = Find h C 2 = a 2 + b 2 b c  a (x) (y)

Sample Problem Find  if h = 701 and x = 125 Cos -1 (x/h) =  Cos -1 (125/701) =   = Find  if h = 24.2 and y = 2.50 Sin -1 (y/h) =  Sin -1 (2.50/24.2)=   = b c  a (x) (y)

Scalene Triangles In the lab you will need to use trig, but you will not have the ability to make the problem fit into a right triangle. In this case, you must use the Law of Cosines

The Law of Cosines C B A

Assignment Finish “Trigonometry for Basic Physics” worksheet for Wednesday. (It will be collected) Read Chapter 3 by 9/24/03 The will be a “quiz” on trig Thursday No more than 5 or 10 points