amaths~~~~~~~~

用戶114616

2007-03-25 3:33 am

http://chingyihouse.linknethost.com/P1010689.JPG

AOB is a sector of radius r and centre O , angle AOC = feta , angle AOB = π / 3 and CD//AO

(a) Express OD in terms of r and feta

(b) Express the area of triangle COD in terms of r and feta

(c) It is claimed that when C is the mid-point of arc AB , the area of triangle COD os maximum . Do you think it is true ? Explain your answer

回答 (1)

jumpover2fence

2007-03-25 6:50 am

✔ 最佳答案

(a) Drop a line from C to OB, intersect at point P.
Then,
angle COB = π / 3 - feta
OP = r cos (π / 3 - feta)
CP = r sin(π / 3 - feta)
DP = CP tan (π / 3) = r sin (π / 3 - feta) tan (π / 3)
OD = OP - DP = r cos (π / 3 - feta)- r sin (π / 3 - feta) tan (π / 3)

(b) triangle COD = triangle COP - triangle CDP
triangle COD = CP * OP/2 - CP * DP/2
= r sin(π / 3 - feta)/2 * (r cos (π / 3 - feta) - r sin (π / 3 - feta) tan (π / 3))

(c) the question is not clear and cannot be understood.

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