a: -1<=sin x<=1

=>-3<=3sin x<=3

=>-3+1<=3sin x+1<=3+1

=>-2<=y<=4

y min=-2 khi sin x=-1

=>\(x=-\frac{\pi}{2}+k2\pi\)

y max=4 khi sinx=1

=>\(x=\frac{\pi}{2}+k2\pi\)

b: -1<=sin x<=1

=>1>=-sin x>=-1

=>1+4>=-sin x+4>=-1+4

=>5>=y>=3

y max=5 khi sin x=-1

=>\(x=-\frac{\pi}{2}+k2\pi\)

y min=3 khi sin x=1

=>\(x=\frac{\pi}{2}+k2\pi\)

c: \(0\le\sqrt{\sin x}\le1\)

=>\(0\le2\cdot\sqrt{\sin x}\le2\)

=>\(0+1\le2\cdot\sqrt{\sin x}+1\le2+1\)

=>1<=y<=3

y min=1 khi sin x=0

=>\(x=k\pi\)

y max=1 khi sin x=1

=>\(x=\frac{\pi}{2}+k2\pi\)

d: \(-1\le cosx\le1\)

=>\(-1\cdot5\le5\cdot cosx\le1\cdot5\)

=>-5<=5cosx<=5

=>-5+1<=5*cosx+1<=5+1

=>-4<=y<=6

y min=-4 khi cosx=-1

=>\(x=\pi+k2\pi\)

y max=6 khi cosx=1

=>\(x=k2\pi\)

e: -1<=cosx<=1

=>2>=-2cosx>=-2

=>2+3>=-2*cosx+3>=-2+3

=>5>=y>=1

y max =5 khi cosx=-1

=>\(x=\pi+k2\pi\)

y min=1 khi cosx=1

=>\(x=k2\pi\)

f: \(0\le\sqrt{cosx}\le1\)

=>\(0\le3\cdot\sqrt{cosx}\le3\cdot1=3\)

=>\(0+4\le3\cdot\sqrt{cosx}+4\le3+4\)

=>4<=y<=7

y min=4 khi cosx=0

=>\(x=\frac{\pi}{2}+k\pi\)

y max=7 khi cosx=1

=>\(x=k2\pi\)

g: \(0\le\sin^2x\le1\)

=>\(0\le4\cdot\sin^2x\le4\)

=>\(0-1\le4\cdot\sin^2x-1\le4-1\)

=>-1<=y<=3

y min=-1 khi \(\sin^2x=0\)

=>sin x=0

=>\(x=k\pi\)

y max=3 khi \(\sin^2x=1\)

=>\(cos^2x=0\)

=>cosx=0

=>\(x=\frac{\pi}{2}+k\pi\)

h: \(0\le cos^2x\le1\)

=>\(0\le9\cdot cos^2x\le9\)

=>\(0-1\le9\cdot cos^2x-1\le9-1\)

=>-1<=y<=8

y min=-1 khi \(cos^2x=0\)

=>cosx=0

=>\(x=\frac{\pi}{2}+k\pi\)

y max=8 khi \(cos^2x=1\)

=>\(\sin^2x=0\)

=>sin x=0

=>\(x=k\pi\)