Trig Chapter 2

Trig Chapter 2

1. 2.1

   • Trigonometric functions are :
     • sinX = (Opposite/Hypotenuse)
       • cscX = (sinX)^-1
     • CosX = (Adjacent / Hypotenuse)
       • sec(X) = (cosX)^-1
     • TanX = Opposite/Adjacent
       • CotX = (TanX)^-1
     • SinX^-1 isn't 1/sinx.
       • (Sinx)^-1 = 1/sinx
   • Triangles = 180°
     • Pythagorean's theorem only applies to right triangles.
   • Similar shapes have the same angles and have sides proportional to each other.
   • estimating roots: lower nearest square root(x), and the difference between the two divided by the difference(y) between the two closest square root (1 higher, 1 lower.)[z]. X+y/z
   • The biggest side is opposite the biggest angle.

2. 2.2

   • The unit circle is a circle of radius 1
     • x^2 + y^2 = 1
     • You can predict the points on the circle (even the ugly ones) using (cosx, sinx) as the points of the angle. (ex: cos 30° = square root 3/ 2
   • if something has a degrees symbol, it's most likely degrees. If It doesn't, it's most likely radians.
   • Reference angle- how far off is the angle from the nearest half circle? Reference angle and the angle always have the same sine and cosine.

3. 2.3

   • 45° = π/4
   • 30°= π/6
     • if the numerator has an even numerator it simplifies down to
       • 60° = π/3
   • sineX = y/1
     • cosineX = x/1
       • Therefore, (cosX)^2 +(sinX)^2 = 1 on the unit circle
     • Tanx = Y/X = sin/cos. THIS IS THE RATIO OF sine to cosine
       • secX = 1/x =1/cosX
         • cscX = 1/y = 1/sinX
           • CotX = x/y = CosX/SinX
   • conditional equation- sometimes is true.
     • Identity equation- always true
   • Tan, Sin, Cos <1 or >-1.
     • Cot, csc, sec >1 or <-1
   • complementary angles swap (x,y) coordinates