Trigonometry Chapter 2, 2.4 & 2.5.

Trigonometry Chapter 2, 2.4 & 2.5.

1. 2.4

   • zeroes can't be canceled
   • Reciprocal identities: Sec = 1/Cos, Csc = 1/Sin, Cot = 1/tan Cos = 1/sec, Sin = 1/csc, Tan = 1/Cot.
   • Pythagorean Identities: sin^2 + cos^2 = 1................. tan^2 +1 = sec^2 ................. 1+Cot^2 = Csc^2
   • f^-1 is the inverse. (f(x))^-1 is 1/f(x)
   • There are two rules when making something an identity/proving it's an identity function. One-nothing can swap sides, they must stay on their respective sides. Two- don't mess with both sides of the equation at the same time. (Ex: Squaring)
   • A handy tip is to convert things to just Sine and Cosine first.

2. 2.5

   • Cos of sides larger than the unit circle is x/√x^2+y^2. (X/the radius)
     • Sine of sides larger than the unit circle is y/√x^2+y^2. (Y/the radius)
       • Suppose an object is traveling on a circular path of radius (r) centered at the origin with triangular velocity w. If t = 0 corresponds to the point (r,0), then the x and y coordinates of the object are functions of t and are given by x=rcos(wt) and y=rsin(wt). Here w>0 indicates a clockwise direction.
         • csc = r/y = √x^2+y^2/y, provided y doesn't equal 0
           • sec = r/x = √x^2+y^2/x, provided x isn't 0
             • tan = y/x, provided x isn't 0
               • cot = x/y, provided y isn't 0