a) `-1 <= sin(x+π/4) <=1`
`<=> -2 <= 2sin(x+π/4)<=2`
`<=> -1 <= 2sin(x+π/4) <= 3`
`=> y_(min) =-1 ; y_(max)=3`
b) `-1<=cosx<=1`
`<=> 0 <= cosx+1 <= 2`
`<=> 0 <=\sqrt(cosx+1) <= \sqrt2`
`<=> 0 <=2\sqrt(cosx+1) <= 2+\sqrt2`
`<=> -3 <= 2\sqrt(cosx+1)-3 <= \sqrt2-1`
`=> y_(min)=-3 ;y_(max)=\sqrt2-1`
c) `y=4sin^2x-4sinx+3=(2sin^2x)-2.2sinx .1 +1^2 +2=(2sinx-1)^2+2`
`-1<=sinx<=1`
`<=>-2<=2sinx<=2`
`<=>-3<=2sinx-1<=1`
`<=>0<=(2sinx-1)^2<=1`
`<=>2<=(2sinx-1)^2+2<=3`
`=> y_(min)=2 ; y_(max)=3`
d) `y=cos^2x+2sinx+2=(1-sin^2x)+2sinx+2=-sin^2x+2sinx+3=-(sinx-1)^2+4`
`-1<=sinx<=1`
`<=> -2<=sinx-1<=0`
`<=>0<=(sinx-1)^2<=4`
`<=> -4<=-(sinx-1)^2<=0`
`<=> 0<=-(sinx-1)^2+4<=4`
`=> y_(min)=0 ; y_(max)=4`
