Finding the Secant of an Angle: A Step-by-Step Guide with Examples

Sec(x)

The secant function, denoted as sec(x), is a trigonometric function that represents the reciprocal of the cosine function

The secant function, denoted as sec(x), is a trigonometric function that represents the reciprocal of the cosine function. It is defined for all real numbers except for values where the cosine function is zero, since division by zero is undefined.

The secant function can be computed using the identity:
sec(x) = 1 / cos(x)

Let’s understand how to find the secant of an angle using this formula:

1. Determine the angle ‘x’ for which you want to find the secant value.

2. Calculate the cosine of the angle ‘x’ using a calculator or trigonometric tables.

3. Once you have the value of cosine, take its reciprocal (i.e., divide 1 by the cosine value).

For example, let’s find the secant of 45 degrees (π/4 radians):

1. x = 45 degrees or π/4 radians.

2. cos(45°) ≈ 0.707 (using a calculator).

3. sec(45°) = 1 / cos(45°) = 1 / 0.707 ≈ 1.414.

So, the secant of 45 degrees is approximately 1.414.

You can follow the same steps to find the secant of any other angle by substituting the corresponding value of ‘x’. Just be aware that when the cosine value is zero at certain angles (e.g., multiples of 90 degrees), the secant function is undefined.

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