Question

find the exact value for cos^-1(cos(-5pi/3))

Answer 1

Do the stuff inside the parenthesis first.

cos(-5π/3) = -1/2

Then work your way outside.

Answer 2

x = cos^-1(-1/2)

cos(x) = -1/2

x = 2π/3 and 4π/3

Answer 3

\[\cos^-1*\cos(5\pi/3)=1.8388\]

Answer 4

the answer key says the answer is pi/3 but I don't know how to do it

Answer 5

okay lets do it this way

Answer 6

Hey I miscalculated there, cos(-5π/3) = 1/2

Answer 7

cosx = 1/2 => x = pi/3 or -pi/3

Answer 8

usually for a function \(f^{-1}\circ f(x)=x\) but not in this case, because \(-\frac{5\pi}{3}\) is not in the range of \(\cos^{-1}(x)\)
the range of \(\cos^{-1}(x)\) is \([0,\pi]\)

Answer 9

so what you are looking for is a number (angle) on the upper half of the unit circle where cosine is the same as it is at \(-\frac{5\pi}{3}\)

Answer 10

that is clearly coterminal with \(\frac{\pi}{3}\) and so that is your answer

Answer 11

btw the answer is NOT \(\frac{\pi}{3}\) or \(-\frac{\pi}{3}\)
arccosine is a well defined function

Answer 12

thanks bro