trigrat
(expression) applies a series
of algorithms to expression.
float(expression)
to the final result.
>> syms x >> trigrat(sin(x)^2+cos(x)^2) ans = 1 >> b=sin(x)^2+sin(x+2*pi/3)^2+sin(x+4*pi/3)^2; >> trigrat(b) ans = 3/2 >> trigrat(i/2*log(x+i*pi)) ans = 1/4*i*log(x^2+pi^2)+(1/2*atan(x/pi)-1/4*pi) >> trigrat(sin((x+y)/2)*cos((x-y)/2)) ans = 1/2*sin(y)+1/2*sin(x) >> trigrat(sqrt(4*y^2+4*x*y-4*y+x^2-2*x+1)) ans = y+(1/2*x-1/2)
trigexpand(expression)
expands trigonometric expressions
to complex exponentials. It is the first step of the function trigrat
above.
>> syms x >> trigexp(i*tan(i*x)) ans = (-exp(2*x)+1)/(exp(2*x)+1) >> trigexp(atan(1-x^2)) ans = -1/2*i*log((-x^2+(1-1*i))/(x^2+(-1-1*i)))