Question

Sec-1 4

Answer 1

Answer:

  1.32

Step-by-step explanation:

Consider ...

  x = sec⁻¹(4) . . . . . the inverse secant function of 4, also written arcsec(4)*

Taking the secant of both sides, we have ...

  sec(x) = 4

Writing this in terms of more familiar functions, it is ...

  1/cos(x) = 4

  cos(x) = 1/4

Now, we can use a calculator to find the inverse function. Be sure the calculator is in the appropriate angle mode. We suspect the desired result is in radians.

  x = cos⁻¹(1/4) ≈ 1.318116

  sec⁻¹(4) ≈ 1.32 . . . . . radians

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* One way to read this is "the angle whose secant is 4." This helps remind you that the result is an angle, so can be in degrees or radians (or any of several other angle measures).