**Inverse Cosine cos ^{-1} Cos^{-1} arccos Arccos**

The inverse function of cosine.

**Basic idea**: To find cos^{-1} (½), we ask "what angle has cosine equal to ½?" The answer is 60°. As a result we say ^{-1} (½) = 60°.^{-1} (½) = π/3.

**More**: There are actually many angles that have cosine equal to ½. We are really asking "what is the simplest, most basic angle that has cosine equal to ½?" As before, the answer is 60°. Thus ^{-1} (½) = 60°^{-1} (½) = π/3.

**Details**: What is cos^{-1} (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus ^{-1} (–½) = 120°^{-1} (–½) = 2π/3.

In other words, the range of ^{-1}

Note: arccos refers to "arc cosine", or the radian measure of the arc on a circle corresponding to a given value of cosine.

__Technical note__: Since none of the six trig functionssine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or ^{-1}).

**See also**

Inverse trigonometry, inverse trig functions, interval notation

Copyrights © 2013 & All Rights Reserved by hltd.org*homeaboutcontactprivacy and policycookie policytermsRSS*