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Inverse Secant sec-1 Sec-1 arcsec Arcsec

The inverse duty of secant.

You are watching: Sec^-1(1)

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

More: There space actually numerous angles that have actually secant equal to 2. We space really questioning "what is the simplest, most basic angle that has secant same to 2?" together before, the price is 60°. Thus sec-1 2 = 60° or sec-1 2 = π/3.

Details: What is sec-1 (–2)? execute we select 120°, –120°, 240° , or some other angle? The prize 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 variety of sec-1 is limited to <0, 90°) U (90°, 180°> or

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. Note: sec 90° is undefined, for this reason 90° is no in the variety of sec-1.

Note: arcsec refers to "arc secant", or the radian measure up of the arc on a circle equivalent to a provided value of secant.

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Technical note: because none the the 6 trig features sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses space not functions. Every trig role can have its domain restricted, however, in bespeak to do its station a function. Part mathematicians compose these limited trig functions and their inverses with an initial capital letter (e.g. Sec or Sec-1). However, most mathematicians execute not follow this practice. This website does no distinguish in between capitalized and uncapitalized trig functions.

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See also

Inverse trigonometry, station trig functions, term notation