secant of theta
The secant of theta, denoted as sec(theta), is a trigonometric function that is defined as the reciprocal of the cosine of theta
The secant of theta, denoted as sec(theta), is a trigonometric function that is defined as the reciprocal of the cosine of theta. In other words, it is the ratio of the hypotenuse to the adjacent side in a right triangle with angle theta.
Mathematically, sec(theta) is given by the formula:
sec(theta) = 1 / cos(theta)
To understand this better, let’s consider an example. Suppose we have a right triangle with angle theta as one of its acute angles. In such a triangle, the hypotenuse is the longest side, the opposite side is the side opposite to the angle theta, and the adjacent side is the side next to the angle theta.
Now, let’s assume that the length of the adjacent side is represented by ‘a’ and the length of the hypotenuse is represented by ‘h’. Using the Pythagorean theorem, we can establish the relationship between these sides:
a² + b² = h²
Now, let’s focus on the cosine of theta:
cos(theta) = a / h
To find the secant of theta, we take the reciprocal of the cosine:
sec(theta) = 1 / cos(theta) = 1 / (a / h) = h / a
So, the secant of theta is the ratio between the hypotenuse and the adjacent side of a right triangle.
It is worth noting that the secant function is periodic, meaning it repeats every 360 degrees or 2π radians. The values of sec(theta) can be positive, negative, or undefined depending on the value of theta and the quadrant in which the angle is located.
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