Question

cos^-1[cos(-3pi/5)]
Why is the value to this expression 3pi/5?

Answer 1

that is because arccos(x) will only give a value between 0 and pi

Answer 2

cos(-3pi/5) = cos(3pi/5)

so, arccos(cos(3pi/5)) = 3pi/5

Answer 3

I know but shouldn't the reference angle be found?

Answer 4

I was totally overthinking it.. so when should I use the reference angle? :0

Answer 5

reference angle is irrelevant. What you need to do is the use the unit cirle

Answer 6

I do use it but none of the values or angles are within their ranges

Answer 7

What you need to understand is that it's always the outer most function that determine the output. In this case it's arccos(x).

arccos(cos(x)) = x ONLY when 0 <= x <= pi

If x is not in that domain, which it is not in this case, then you need to find a different angle whose cosine is the same.



According to the unit circle, it's clear that cos(-3pi/5) = cos(3pi/5), and since
0 <= 3pi/5 <= pi, 3pi/5 is the value you'll get at the end

Answer 8

well that explains a lot. 3pi/5 (108 degrees) is in the 2nd quadrant? I was a little confused by that as well but because its past 90degrees i can see why it would be. I just want to make sure