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Caculatesec (θ)

θ angle




sec(θ)

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In a right angled triangle, Secant of an angle is the ratio of the length of the hypotenuse to the length of the adjacent side.

Formula

To find the Secant of a given angle θ , use the following formula.

\( sec(θ) = \frac{Length~ of~ Hypotenuse}{Length~ of~ Adjacent~ side} \)

Calculating Secant of an Angle

The secant (sec) of an angle in a right triangle is a trigonometric function that represents the ratio of the length of the hypotenuse to the adjacent side. It is the reciprocal of the cosine function. This function is often used to find unknown side lengths or angles in right triangles.

The secant of an angle \( \theta \) is defined as:

\( \sec(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}} \)

where:

Example 1

Let's calculate the secant of a 30-degree angle:

In a right triangle, if the angle \( \theta = 30^{\circ} \), the adjacent side is \( \sqrt{3} \) times half the length of the hypotenuse. So, the secant of 30 degrees is:

\( \sec(30^{\circ}) = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{1}{\cos(30^{\circ})} = \frac{1}{0.866} \approx 1.154 \)

Example 2

Consider another example with a 45-degree angle:

In a right triangle, if the angle \( \theta = 45^{\circ} \), the adjacent side and the opposite side are of equal length, and the hypotenuse is \( \sqrt{2} \) times the length of the adjacent side. So, the secant of 45 degrees is:

\( \sec(45^{\circ}) = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{1}{\cos(45^{\circ})} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2} \approx 1.414 \)

These examples demonstrate how to calculate the secant of an angle manually, showing the importance of understanding the trigonometric function secant in various mathematical and practical applications.