Inverse Sec
1/xsqrt(x^2-1)
The inverse secant function, denoted as Arcsec or Sec^-1, is the inverse function of the secant function. Its domain is the set of all real numbers except for -1 ≤ x ≤ 1, since the secant function is not defined for those values.
The inverse secant function takes an input value and returns the angle in radians that has a secant value equal to that input. In other words, if y = sec^-1(x), then x = sec(y), where y is the angle measure in radians.
The graph of the inverse secant function appears to be a reflection of the graph of the secant function about the line y = x. The range of the inverse secant function is [0, π/2) ∪ (π/2, π], which means that the output value is always between 0 and π.
Some key properties of the inverse secant function include:
– It is an odd function, meaning that sec^-1(-x) = -sec^-1(x).
– It is a decreasing function on its domain.
– It is undefined for x = -∞ and x = ∞.
To evaluate the inverse secant function at a specific value, one approach is to use a calculator or computer software that has the function built-in. Alternatively, you can use the identity sec(y) = 1/cos(y) and find the angle whose cosine equals the reciprocal of your input value. Then, convert the angle measure from degrees to radians if necessary.
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