更新1:
For 0≦a≦90,the least value of 30/(3(sin a)^2+2(sin(90-a))^2) is?
For 0≦a≦90,the least value of 30/3(sin a)^2+2(sin(90-a))^2 is?
回答 (1)
2016-09-08 5:10 am
Sol
3Sin^2 a+2Sin^2 (90-a)
=3Sin^2 a+2Cos^2 a
=2+Sin^2 a
0<=a<=90度
0<=Sina<=1
0<=Sin^2 a<=1
2<=2+Sin^2 a<=3
1/3<=1/(2+Sin^2 a)<=1/2
1/3<=1/[3Sin^2 a+2Sin^2 (90度－a)]<=1/2
30/3<=30/[3Sin^2 a+2Sin^2 (90度－a)]<=30/2
10<=30/[3Sin^2 a+2Sin^2 (90度－a)]<=15
3Sin^2 a+2Sin^2 (90-a)
=3Sin^2 a+2Cos^2 a
=2+Sin^2 a
0<=a<=90度
0<=Sina<=1
0<=Sin^2 a<=1
2<=2+Sin^2 a<=3
1/3<=1/(2+Sin^2 a)<=1/2
1/3<=1/[3Sin^2 a+2Sin^2 (90度－a)]<=1/2
30/3<=30/[3Sin^2 a+2Sin^2 (90度－a)]<=30/2
10<=30/[3Sin^2 a+2Sin^2 (90度－a)]<=15
收錄日期: 2021-04-18 15:33:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160907205028AA3oWwh