Pi := 3.14159;
vardef torad expr x = Pi*x/180 enddef;       % conversions
vardef todeg expr x = 180x/Pi enddef;
vardef sin expr x = sind(todeg(x)) enddef;   % radians version of sind
vardef cos expr x = cosd(todeg(x)) enddef;   % and cosd

vardef sign expr x = if x>=0: 1 else: -1 fi enddef; % commodity

vardef tand expr x =                      % tan with arg in degree
  if cosd(x) = 0:
    infinity * sign(sind(x))
  else: sind(x)/cosd(x) fi enddef;
vardef tan expr x = tand(todeg(x)) enddef; % arg in rad

% INVERSE

% the arc having x as tanget is that between x-axis and a line
% from the center to the point (1, x); MF angle says this
vardef atand expr x = angle(1,x) enddef;
vardef atan expr x = torad(atand(x))  enddef;  % rad version

% known formula to express asin and acos in function of
% atan; a+-+b stays for sqrt(a^2 - b^2) (defined in plain MF)
vardef asin expr x =  2atan(x/(1+(1+-+x)))  enddef;
vardef acos expr x =  2atan((1+-+x)/(1+x))  enddef;

vardef asind expr x =  todeg(asin(x))  enddef; % degree versions
vardef acosd expr x =  todeg(acos(x))  enddef;

% commodity
def outcompare(expr a, b) = message decimal a & " = " & decimal b enddef;

% output tests
outcompare(torad(60), Pi/3);
outcompare(todeg(Pi/6), 30);

outcompare(Pi/3, asin(sind(60)));
outcompare(30, acosd(cos(Pi/6)));
outcompare(45, atand(tand(45)));
outcompare(Pi/4, atan(tand(45)));

outcompare(sin(Pi/3), sind(60));
outcompare(cos(Pi/4), cosd(45));
outcompare(tan(Pi/3), tand(60));

end