Question

what does cos^-1 mean?

Answer 1

if cos (x) = adjacent/hypotenuse, then x = cos^-1(adjacent/hypotenuse)

Answer 2

\[\cos ^{-1}x\]means the inverse of cosine.

Answer 3

Suppose that\[cosy =x\]then\[y =\cos ^{-1}x\]In other words if the cosine of an angle is x, then the inverse cosine of x is the angle y.

Answer 4

yes but why does it change to cos^-1.... wouldnt htat be the same as 1/cos ?

Answer 5

no, thats just the notation for it. 1/cosine is actually secant. two different functions. if its cos^-1(x) its the inverse, and if its (cos(x))^-1 then its secant

Answer 6

Example: If\[\cos \theta \approx 0.7071\]then\[\theta = \cos ^{-1}(0.7071)\]Therefore\[\theta =45° \]

Answer 7

isn't that the same as arccos

Answer 8

\(^{-1}\) is notation for inverse. It isn't always multiplicative inverse (reciprocal).

Answer 9

Yes correct!\[\cos ^{-1}x =arc cosx\]

Answer 10

I always preferred the name, "arc-cosine" because it does tell you the arc of the central angle.

Answer 11

Yes, I believe I already explained that it means inverse, elegantly.

Answer 12

That is true, it is the arc of a central angle.

Answer 13

LOL, yes, very elegantly indeed.