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Inverse Secant sec-1 Sec-1 arcsec Arcsec

The inverse feature of secant.

You are watching: Sec^-1(-2)

Basic idea: To uncover sec-1 2, we ask "what angle has actually secant equal to 2?" The answer is 60°. As an outcome we say that sec-1 2 = 60°. In radians this is sec-1 2 = π/3.

More: Tbelow are actually many type of angles that have actually secant equal to 2. We are really asking "what is the easiest, many basic angle that has actually secant equal to 2?" As before, the answer is 60°. Thus sec-1 2 = 60° or sec-1 2 = π/3.

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

In various other words, the selection of sec-1 is minimal to <0, 90°) U (90°, 180°> or

. Note: sec 90° is uncharacterized, so 90° is not in the range of sec-1.

Note: arcsec describes "arc secant", or the radian meacertain of the arc on a circle matching to a provided value of secant.

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Technical note: Due to the fact that none of the 6 trig features sine, cosine, tangent, cosecant, secant, and also cotangent are one-to-one, their inverses are not attributes. Each trig function can have its doprimary minimal, however, in order to make its inverse a function. Some mathematicians create these restricted trig attributes and also their inverses through an initial capital letter (e.g. Sec or Sec-1). However, a lot of mathematicians execute not follow this exercise. This website does not identify between capitalized and also uncapitalized trig features.


See also

Inverse trigonomeattempt, inverse trig functions, interval notation