Understanding the Secant Function | Definition, Calculation, and Relationship with Cosine and Sine

int secx

In mathematics, ‘sec x’ represents the secant function

In mathematics, ‘sec x’ represents the secant function. The secant function is a trigonometric function that is the reciprocal of the cosine function. It is defined for all real numbers except for the points where cosine is zero, as division by zero is undefined.

To find the value of sec x, you first need to calculate the cosine of x, denoted as cos x. Once you have the cosine value, you can take the reciprocal of it to get the secant value. Mathematically, it can be represented as:

sec x = 1 / cos x

For example, let’s say you want to find the value of sec(45°). First, you calculate the cosine of 45°, which is equal to √2/2 or approximately 0.7071. Taking the reciprocal of this value, you get:

sec(45°) = 1 / (√2/2) = 2 / √2 = √2

Therefore, sec(45°) is equal to √2.

Note that sec x can also be expressed in terms of the sin function:

sec x = 1 / cos x = 1 / √(1 – sin^2 x)

This alternate representation allows us to understand the relationship between the secant and sine functions.

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