a brief summary of circular functions and trigonometry

Introduction

NB. π radians = 180 degrees.
unit circle defined by x²+y² = 1 and each point of the circle represented by (cost,sint) where t = angle in radians polar coordinates which is also twice the area of the sector subtended by that angle
- ie. cos(t)²+sin(t)² = 1
tanx=sinx/cosx, cosx not= 0;
cotx=cosx/sinx;
secx=1/cosx;
cosecx=1/sinx;
1+(tan²)x = (sec²)x, cosx not= 0;
1+(cot²)x = (cosec²)x, sinx not= 0;
(cos²)x + (sin²)x = 1;
Where x is in degrees:
- sin(90-x) = cosx; cos(90-x) = sinx;
- tan(90-x) = cotx; cot(90-x) = tanx;
- sin(180-x)= sinx; cos(180-x)=-cosx;
- tan(180-x)=-tanx; cot(180-x)=-cotx;
- sin(180+x)=-sinx; cos(180+x)=-cosx;
- tan(180+x)= tanx; cot(180+x)= cotx;
- sin(360-x)=-sinx; cos(360-x)= cosx;
- tan(360-x)=-tanx; cot(360-x)=-cotx;
- sin(-x) =-sinx; cos(-x) = cosx;
- tan(-x) =-tanx; cot(-x) =-cotx;
- sin(x+y) = sinxcosy + cosxsiny;
- sin(x-y) = sinxcosy - cosxsiny;
- cos(x+y) = cosxcosy - sinxsiny;
- cos(x-y) = cosxcosy + sinxsiny;
- tan(x+y) = (tanx + tany)/(1 - tanxtany);
- tan(x-y) = (tanx - tany)/(1 + tanxtany);
- sin2x = 2sinxcosx = 2tanx/(1 + (tan^2)x);
- cos2x = (cos²)x - (sin²)x = 2(cos²)x - 1;
  - = 1-2(sin²)x = (1-(tan²)x)/(1+(tan²)x);
- tan2x = 2tanx/(1 - (tan²)x);
- 2sinxcosx = sin(x+y) + sin(x-y);
- 2cosxcosy = cos(x+y) + cos(x-y);
- 2sinxsiny = cos(x-y) - cos(x+y);
- sinx + siny = 2sin((x+y)/2)cos((x-y)/2);
- sinx - siny = 2cos((x+y)/2)sin((x-y)/2);
- cosx + cosy = 2cos((x+y)/2)cos((x-y)/2);
- cosx - cosy =-2sin((x+y)/2)sin((x-y)/2);

NB. Must restrict circular function to make 1-to-1:
- ie. sinx, xE[-90,90]; cosx, xE[0,180]; tanx, -90<x<90;
General Solutions:
- sinx = a, ⇒ x = 180n + ((-1)ⁿ)Arsina;
- cosx = a, ⇒ x = 360n +/- Arcosa;
- tanx = a, ⇒ x = 180n + Artana;