Câu hỏi của Trâm Phạm

Question

Tìm GTLN GTNN của hàm số

a, y=3-2sin(x+pi/6)

b, y=2(sin⁴x+cos⁴x) +3

c, y=4sinx.cosx -1

d, y= 2sin.3x +1

e, y= 4-3sin².2x

Nguyễn Việt Lâm · Accepted Answer

a.

Do $-1\le sin\left(x+\frac{\pi}{6}\right)\le1\Rightarrow1\le y\le5$

$y_{min}=1$ khi $sin\left(x+\frac{\pi}{6}\right)=1$

$y_{max}=5$ khi $sin\left(x+\frac{\pi}{6}\right)=-1$

b.

$y=2\left[\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x\right]+3$

$y=2-4sin^2x.cos^2x+3=5-sin^22x$

Do $0\le sin^22x\le1\Rightarrow4\le y\le5$

$y_{min}=4$ khi $sin^22x=1$

$y_{max}=5$ khi $sin^22x=0$Câu trả lời: a.

Do $-1\le sin\left(x+\frac{\pi}{6}\right)\le1\Rightarrow1\le y\le5$

$y_{min}=1$ khi $sin\left(x+\frac{\pi}{6}\right)=1$

$y_{max}=5$ khi $sin\left(x+\frac{\pi}{6}\right)=-1$

b.

$y=2\left[\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x\right]+3$

$y=2-4sin^2x.cos^2x+3=5-sin^22x$

Do $0\le sin^22x\le1\Rightarrow4\le y\le5$

$y_{min}=4$ khi $sin^22x=1$

$y_{max}=5$ khi $sin^22x=0$

Nguyễn Việt Lâm · Answer

c.

$y=2sin2x-1$

Do $-1\le sin2x\le1\Rightarrow-3\le y\le1$

$y_{min}=-3$ khi $sin2x=-1$

$y_{max}=1$ khi $sin2x=1$

d.

$-1\le sin3x\le1\Rightarrow-1\le y\le3$

e.

$0\le sin^22x\le1\Rightarrow1\le y\le4$Câu trả lời: c.

$y=2sin2x-1$

Do $-1\le sin2x\le1\Rightarrow-3\le y\le1$

$y_{min}=-3$ khi $sin2x=-1$

$y_{max}=1$ khi $sin2x=1$

d.

$-1\le sin3x\le1\Rightarrow-1\le y\le3$

e.

$0\le sin^22x\le1\Rightarrow1\le y\le4$

Bài 1: Hàm số lượng giác