Chapter 5

Chapter 5

1. 5.1 & 5.2

   • an inverse will look like a reflection over y=x
     • THIS IS cos^-1(x) AND sin^-1(x)
       • Inverse swaps the domain and range of what is being mirrored over y=x.
         • You can only have half a period worth, so sin^-1(x) is the right half of a circle and cos^-1(x) is the top half of a circle.
           • When graphing, swap the positions of the x and y coordinates when going from regular to inverse functions
             • the inverse of sin and cos and its regular function will cancel each other out to the lowest common angle/radian (probably in radians). Ex sin^-1(sin(9pi/4)) = sin^-1((square root of 2)/2)= pi/4
               • Inverse trig functions take in a ratio and spit out an angle. Regular trig functions take in an angle and spit out a ratio.
                 • Inverse undoes what Regular trig functions do
   • Tanx^-1(x) & Cotx^-1(x)
     • Cot is in the top half and Tan is in the right half.
       • with inverse function, the inputs flip with regular functions the outputs flip
         • when graphing inverses generally choose the positive line closest to zero.

2. 5.3 & 5.4

   • Use the buttons right ya dingus
     • 2nd and the corresponding Trig Function
   • cos^-1(1/x) = sec^-1(x), Top side
     • sin^-1(1/x)= csc^-1(x) Right side.
       • tan^-1(1/x) = cot^-1(x) top half

3. when solving for something, it is incorrect to say "multiply by Cos/sin/tan" both sides since actually you're applying that to both sides.