Question

if you wanna find the principle value for cos^-1 root3/2 its pi/6

but if you wanna find cos^-1(-1/2) you gotta use pi - pi/3

Why should you use pi - pi/3 for -1/2 but not root3/2?

Answer 1

@bloopman

Answer 2

idk sorry :/ lol

Answer 3

aw its okay :(

Answer 4

cos(x)=y was restricted on the interval [0,pi] so the function f(x)=cos(x)
could be one-to-one and therefore have an inverse function some people like to notate as f(x)=arccos(x)

Answer 5

\[\cos^{-1}(\frac{\sqrt{3}}{2})=\frac{\pi}{6} \text{ we can see from our picture this is true }\]

Answer 6

\[\cos^{-1}(\frac{-1}{2})=\frac{2 \pi}{3} \text{ from our picture }\]

Answer 7

which as you say is equal to pi-(pi/3)