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Inverse Secant sec-1 Sec-1 arcsec Arcsec

The inverse role of secant.

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

Basic idea: To uncover sec-1 2, we ask "what angle has secant same to 2?" The price is 60°. As a result we say the sec-1 2 = 60°. In radians this is sec-1 2 = π/3.

More: There are actually numerous angles that have secant equal to 2. We are really asking "what is the simplest, most an easy angle that has actually secant same to 2?" as before, the answer is 60°. For this reason sec-1 2 = 60° or sec-1 2 = π/3.

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

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

. Note: sec 90° is undefined, therefore 90° is not in the variety of sec-1.

Note: arcsec describes "arc secant", or the radian measure of the arc ~ above a circle corresponding to a provided value that secant.

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Technical note: since none the the six trig functions sine, cosine, tangent, cosecant, secant, and also cotangent are one-to-one, your inverses room not functions. Every trig role can have actually its domain restricted, however, in order to do its inverse a function. Part mathematicians compose these limited trig functions and their inverses through an initial resources letter (e.g. Sec or Sec-1). However, many mathematicians execute not follow this practice. This website does not distinguish between capitalized and also uncapitalized trig functions.

See also

Inverse trigonometry, train station trig functions, interval notation