Hello just got a couple problems I'm stuck on. Seeking some help.

csc^-1x = sin^-1 (1/x)

and

sec^-1(x) = cos^-1 (1/x)

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- Apr 23rd 2008, 11:40 AMDaddycakesTrig Identities
Hello just got a couple problems I'm stuck on. Seeking some help.

csc^-1x = sin^-1 (1/x)

and

sec^-1(x) = cos^-1 (1/x) - Apr 23rd 2008, 11:44 AMo_O
Let $\displaystyle y = \sin^{-1} x$.

So:

$\displaystyle \sin y = x$

$\displaystyle \frac{1}{\sin y} = \frac{1}{x}$

$\displaystyle \csc y = \frac{1}{x}$

$\displaystyle y = \csc^{-1} \left(\frac{1}{x}\right)$ - Apr 24th 2008, 08:39 AMDaddycakes
Would the second question have the same set up as the previous.

Show that the following identity is true

sec-1x = cos-1 (1/x)

let y= cos^-1

cosy=x

1/cosy=1/x

secy=1/x

y= sec^-1 (1/x)

(Thinking) - Apr 24th 2008, 09:52 AMo_O
Yep. Don't doubt yourself!

- Apr 24th 2008, 10:40 AMDaddycakes
Thanks. I will work on that not doubting myself part as I continue to work through some more of these.