Question

Write the trigonometric expression as an algebraic expression in u.
cos (sin^-1 u) Explain please!

Answer 1

now this is a triangle one

Answer 2

there is picture of an angle whose sine is \(u\)
you need the other leg, which, by pythagoras, is \(\sqrt{1-u^2}\)

Answer 3

if you think about it you knew this already
it is like saying "if the sine is \(u\) what is the cosine?"
if you call the cosine \(a\) then by pythagoras you have
\[a^2+u^2=1\] and so \(a=\sqrt{1-u^2}\)

Answer 4

only in this case you don't have to worry about that pesky \(\pm\) business

Answer 5

Alrighty o: And so whether it is sin, cos, ect, that determines where the u will be in the triangle?