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Calculate csc−1

x= hypotenuse/opposite_side




csc−1(x)

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

Formula

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

θ = csc−1(Length_of_Hypotenuse / Length_of_Opposite_side)

Calculate Csc Inverse

The inverse cosecant (csc-1 or arccsc) of a value is the angle whose cosecant is the given value. It is used to find angles when the cosecant value is known.

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

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

where:

Example 1

Let's calculate the inverse cosecant of 2:

The angle whose cosecant is 2 is 30 degrees or \( \frac{\pi}{6} \) radians. So:

\( \csc^{-1}(2) = 30^{\circ} = \frac{\pi}{6} \)

Example 2

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

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

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

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