< is 大過or等於
1) For 0度< X <360度,how many distinct roots does the equation cosX(sinX-1)=0 have
A.2
B.3
C.4
D.5
maths mc
2007-04-25 1:13 am
回答 (2)
2007-04-25 4:33 am
✔ 最佳答案
答案是ACOS X = 0 or SIN X = 1
COS X = 0
X = 90 or 270 degrees
SIN X = 1
X = 90 degrees
So X = 90 or 270 degrees (only 2 distinct roots)
2007-04-25 3:14 am
cosX(sinX- 1) = 0
cosX = 0
X = 90度 or 360 - 90 =270 度
or sinX -1 = 0
sinX = 1
X = 90度 or 180- 90=90度
( only one root X=90 )
cos is positive in region I & IV
sin is positive in region I & II
Therefore, the equation have 3 distnct roots ( For 0<360 , X 大過0, 但不等於0 )
cosX = 0
X = 90度 or 360 - 90 =270 度
or sinX -1 = 0
sinX = 1
X = 90度 or 180- 90=90度
( only one root X=90 )
cos is positive in region I & IV
sin is positive in region I & II
Therefore, the equation have 3 distnct roots ( For 0<360 , X 大過0, 但不等於0 )
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