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The solutions to group work problems 1-3 in math 412 during spring 2009. Problem 1 involves deriving the formula for arccos z using the same method as for arcsin z. In problem 2, we differentiate both sides of the equation z = cos(arccos z) with respect to z to find the derivative of arccos z. Lastly, problem 3 asks to find all values of arccos 3i.
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Math 412 Group Work #11 Spring 2009
Problem 1. In class, we derived the formula
arcsin z = โi log
iz + (1 โ z 2 ) 1 / 2
Using the same procedure (yes, you can peek at your notes!) derive the formula
arccos z = โi log
z + (z 2 โ 1) 1 / 2
Problem 2. Differentiating both sides of the equation z = cos(arccos z) with respect
to z, derive the formula
d
dz
(arccos z) = โ
(1 โ z^2 )^1 /^2
Problem 3. Find all values of arccos 3i.
