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Inverse Cosine cos-1 Cos-1 arccos Arccos

The inverse function of cosine.

You are watching: Cos(1/2)

Basic idea: To find cos-1 (½), we ask "what angle has actually cosine same to ½?" The answer is 60°. As a an outcome we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.

More: There space actually numerous angles that have cosine same to ½. We space really questioning "what is the simplest, most an easy angle that has cosine equal to ½?" together before, the answer is 60°. For this reason cos-1 (½) = 60° or cos-1 (½) = π/3.

Details: What is cos-1 (–½)? do we select 120°, –120°, 240°, or some various other angle? The answer is 120°. Through inverse cosine, we choose the angle on the top fifty percent of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.

In other words, the selection of cos-1 is minimal to <0, 180°> or <0, π>.

Note: arccos describes "arc cosine", or the radian measure of the arc on a circle equivalent to a offered value the cosine.

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Technical note: since none of the six trig features sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, your inverses space not functions. Each trig role can have its domain restricted, however, in bespeak to do its train station a function. Part mathematicians create these minimal trig functions and also their inverses through an initial funding letter (e.g. Cos or Cos-1). However, many mathematicians carry out not follow this practice. This website does not distinguish in between capitalized and uncapitalized trig functions.


See also

Inverse trigonometry, train station trig functions, term notation