Question

y=sinxcosx的最大值和最小值以及周期

Answer 1

y=sinxcosx

=(sin2x)/2

ymax=1 ;ymin=-1 ;T=2π/2=π

y=3cos²x+sin2x/2

=3(1+cos2x)/2+sin2x/2

=3cos2x/2+sin2x/2+3/2

=√[(3/2)²+(1/2)²]sin(2x+θ)+3/2

=√10sin(2x+θ)/2+3/2

ymax=(√10+3)/2 ;ymin=(3-√10)/2 ;T=2π/2=π