All categories - 21 March 2007

This is the question and my working out, can anyone please tell me if its correct? Thanks.

cos(z) = sqrt(2)

so

z = cos^(-1)(sqrt(2))

now cos^(-1)(z) = -i * log(z+i(1-z^2)^(1/2))

and z = sqrt(2)

so cos^(-1)(z) = i log(sqrt(2) + i(1-2)^(1/2))
= i * log(sqrt(2) + i * i)
= i * log(sqrt(2) -1)

Is that it?

also, heaps of you guys change log into ln, when is it okay to do that - for example in my answer? Can I just change it?


Thanks, Laura

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