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Calculate sec−1

x= hypotenuse/adjacent_side




sec−1(x)

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Inverse Cosine sec−1() is used to find the angle for a given ratio of the length of the hypotenuse to the length of the adjacent side, in a right angled triangle.

Formula

To find the Inverse Secant of a given ratio: hypotenuse/adjacent_side , use the following formula.

θ = sec−1(Length_of_Hypotenuse / Length_of_Adjacent_side)

Calculate Sec Inverse

The inverse secant (sec-1 or arcsec) of a value is the angle whose secant is the given value. It is used to find angles when the secant value is known.

The inverse secant of a value \( y \) is defined as:

\( \sec^{-1}(y) = \theta \)

where:

Example 1

Let's calculate the inverse secant of 2:

The angle whose secant is 2 is 60 degrees or \( \frac{\pi}{3} \) radians. So:

\( \sec^{-1}(2) = 60^{\circ} = \frac{\pi}{3} \)

Example 2

Consider another example with the value \( \sqrt{2} \):

The angle whose secant is \( \sqrt{2} \) is 45 degrees or \( \frac{\pi}{4} \) radians. So:

\( \sec^{-1}(\sqrt{2}) = 45^{\circ} = \frac{\pi}{4} \)

These examples demonstrate how to calculate the inverse secant of a value.