Question

已知函数f(a)=(sina-cosa)sina,a大于或等于0度小于或等于180度,则f(a)的单调增区间是?请详解.

Answer 1

f(a)=1-cosa*cosa-cosa*sina=1-(1+cos2a)/2-(sin2a)/2=(1-sin2a-cos2a)/2

=1/2-根2*sin(2a+pi/4)/2

(2a+pi/4)区间为[pi/4,9pi/4],

sin(2a+pi/4) 单减区间[pi/4,5pi/4],

f(x)单调增区间是[0,pi/2]