This came up when I was trying to evaluate to a decimal value an arcsec(something), but on TI-83 there is no inverse secant button. So, I punched 1/(arccos(something)). Naturally, this came up as a domain error. Then my instructor pointed out arcsesc is not 1/arccosx. Oops. Thinking about it, the domain of the cos-1x is [-1,1]. The domain the sec-1x is (-∞,-1]U[1,∞). So although secx =1/cosx is an identity, it could not be the case for the inverses since there is a discrepancy in domain. Also, the inverse cosine is the function which takes the y value and maps it to the x value, e.g cos-1(1/2) = ∏/3. The inverse secant for this domain value of 1/2 would be...well it wouldn't be since this value is not in the domain of the arcsec! That is an example of why the arcsec is not the multiplicative inverse of arccos. Is there anything I should add or other pressing points or ways of looking at this?