Find the secant of an angle making use of the sec calculator below. Begin by beginning the edge in degrees or radians.

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How to find the Secant of one Angle

In a right triangle, the secant of angle α, or sec(α), is the ratio between the angle’s surrounding side and the hypotenuse.


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Secant is a trigonometric role abbreviated sec. Usage the formula listed below to calculate the secant of an angle.

Secant Formula

The secant formula is:

sec(α) = hypotenuse cadjacent b

Thus, the secant of angle α in a best triangle is same to the size of the hypotenuse c split by the surrounding side b.

To resolve sec, simply enter the size of the hypotenuse and surrounding side, climate solve.

This formula could look very similar to the formula to calculation cosine. That’s because secant is the reciprocal of cosine.

Secant must not be puzzled with arccos, which is the inverse of the cosine function. The difference being the secant is equal to 1cos(x), while arccos is the station of the cosine function.

sec(x) = 1cos(x) = cos(x)-1arccos(y) x wherein y = cos(x)


For example, let’s calculation the secant of edge α in a triangle v the length of the hypotenuse equal to 8 and also the nearby side same to 6.

sec(α) = 86sec(α) = 43


Secant Graph

If girlfriend graph the secant role for every possible angle, it develops a collection of repeating U-curves.


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One crucial property to keep in mind in the graph above is the the secant the an angle is never in the variety of -1 to 1; it’s always smaller 보다 or same to -1 or bigger than or same to 1.

You’ll also an alert that the curves never ever cross the x-axis at an also multiple the 1/2π + π radians, or 90° + 180°

Secant Table

The table below shows usual angles and also the sec worth for every of them.

Table showing common angles and also sec worths for each.

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Angle (degrees)Angle (radians)Secant
01
15°π12√6 – √2
30°π62√33
45°π4√2
60°π32
75°5π12√6 + √2
90°π2undefined
105°7π12-√6 – √2
120°2π3-2
135°3π4-√2
150°5π6–2√33
165°11π12-√6 – √2
180°π-1
195°13π12-√6 – √2
210°7π6–2√33
225°5π4-√2
240°4π3-2
255°17π12-√6 – √2
270°3π2undefined
285°19π12√6 + √2
300°5π32
315°7π4√2
330°11π62√33
345°23π12√6 – √2
360°undefined

You might also be interested in our cosecant and cotangent calculators.


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