7a) Show that √2 cos y + √3 sin y can be written in the form r cos ( y - x ), where r > 0 and x is acute. Find the values of r and x. ( ans : r=√5 ; x = 50.8 )
b) Hence, find the maximum value of √2 cos y + √3 sin y and the smallest positive value of y at which a maximum occurs.
c) Find the minimum value of 1/(√2 cos y + √3 sin y) and the smallest positive value of y at which a minimum occurs.
**Do b + c only
Maths唔識抵死題 (Do it!!)
2010-09-23 6:37 am
回答 (1)
2010-09-23 7:56 am
✔ 最佳答案
a) I would lke to remind you that to turn the cos y+sin y into cos (y-x), x is needed to write as radian.b) as √2 cos y + √3 sin y = √5cos(y-x), for maximum value of cos is equal to 1, so the maximum value = √5 at (y-x)=0, so y=x
c) for minimum value of 1/(√2 cos y + √3 sin y) = 1/√5cos(y-x), for minimum value, cos(y-x) is needed to equal to 1, so it is the same, y = x.
參考: cos 0 = 1
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