Homework SourseI have ft2sint2cos2t but I dont know how to set this equal t
I have f\'(t)=-2sin(t)+2cos(2t) but I don\'t know how to set this equal to 0 in order to fin the critical points. could someone please show me how to do this IN DETAIL please. thanks.
Solution
-2sin(t)+2cos(2t)=0 so 2cos(2t)=2sin(t) so cos(2t)=sin(t) plug in double angle formula: 1-2*sin^2(t)=sin(t) 2*sin^2(t)+sin(t)-1=0 So (2*sin(t)-1)*(sin(t)+1)=0 sin(t)=1/2 or sin(t)=-1 so t =sin^-1(1/2) or sin^-1(-1) so t=pi/6 or t=-pi/2
