Math Is Fun Forum

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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JaneFairfax

Member

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)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: cos(sin-¹(x)) = ?

thanks

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The Beginning Of All Things To End.
The End Of All Things To Come.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: cos(sin-¹(x)) = ?

That is amazing