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#1 2008-02-18 23:29:55

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

cos(sin-¹(x)) = ?

according to my book as part of an answer, it is equal to √(1-x^2) which seems to be related to the derivitive of the inverse sine, but im confused at how to actual derive that. Its came up in alot of the questions in my book needing to do this, but i dont want to know how to derive it.

any help?


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#2 2008-02-19 02:33:39

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: cos(sin-¹(x)) = ?


If we take the range of sin[sup]−1[/sup]x to be

, then its cosine will be non-negative; hence

Last edited by JaneFairfax (2008-02-19 02:43:17)

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#3 2008-02-19 05:26:45

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: cos(sin-¹(x)) = ?

thanks smile


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#4 2008-02-19 21:43:26

Identity
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Registered: 2007-04-18
Posts: 934

Re: cos(sin-¹(x)) = ?

That is amazing

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