Question

If I was given something like:

sin(arccos(something))

How would i find the exact value of that?
and example we had in class was:
sin(arccos(1/2)) = sin(pi/4) = (sqrt3/2)

but i haven't a clue how we got there.

Answer 1

arccos(1/2) is an angle.. It is asking which angle has a cos of 1/2 which is pi/4. so now you have the sin of pi/4 which is squrt 3/2

Answer 2

well with the question you have you can just compute, because
\[\arccos(\frac{1}{2})\] is a number known to you, but you could also find
\[\sin(\arccos(x))\] in terms of x

Answer 3

the picture shows an angle whose cosine is x
that is
\[\arccos(x)\] then by pythagoras you can see that
\[\sin(\arccos(x))=\sqrt{1-x^2}\]

Answer 4

So, if I was given another value of x in the sin(arccos(x)) equation, I could get the value by plugging it into that?