For 0 ° smaller or equal than x smaller or equal 360°, how many roots does the equation cosine to the power three=cosx gave?
Please help and pls show workings, thanks alot !!!!!!!
(urgent!)F.4 maths
2008-04-01 4:07 am
回答 (1)
2008-04-01 4:33 am
✔ 最佳答案
cos(^3)x = cosxcos(^3)x - cosx = 0
cosx (cos(^2)x - 1) = 0
cosx (cosx-1) (cosx+1) = 0
therefore,
cosx = 0
x=90 or 270 (2 roots)
or cosx - 1 = 0
cosx = 1
x=0 or 360 (2 roots)
or cosx + 1 = 0
cosx = -1
x=180 (1 root)
hence, there can be 5 roots to the equation.
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