In mathematics, trigonometry is a crucial topic that is studied by students in various grades. Trigonometric ratios are ratios of the sides of a right triangle to its angles, and they are used to solve problems related to angles, distances, and heights. In this article, we will discuss the reciprocal of cosine or secant, which is an important aspect of trigonometry.
Reciprocal of Cos function
The reciprocal of cosine is secant. It is denoted as sec ?, where ? is the angle between the hypotenuse and adjacent side of a right triangle. The secant is the inverse of the cosine, which means that it is obtained by taking the reciprocal of the cosine.
So,
$cos \theta = \frac {BC}{AC} = \frac {B}{H}$
The formula for the secant is:
sec ? = 1/cos ?
So,
$sec \theta = \frac {AC}{BC} = \frac {H}{B}
The secant is used to find the length of the hypotenuse of a right triangle, given the length of the adjacent side and the angle between the hypotenuse and adjacent side.
Domain and Range of Reciprocal of Cos
- y=f(x)=sec(x)= 1/cos(x)
- Domain of Secant Function: It is defined for all real values of x except x ?(2n + 1)(?/2) where n is any integer as that cos becomes zero
- Range of Secant Function: (-?,-1] ? [1,?)
- Period of Secant Function: 2?
- It is even function
Graph of Reciprocal of cos
Sample Questions
- Find the value of sec 60 degrees.
Solution: We know that the value of cos 60 degrees is 1/2. Therefore, the value of sec 60 degrees is 1/(1/2) = 2.
- If cos ? = 3/5, find the value of sec ?.
Solution: We know that sec ? = 1/cos ?. Therefore, sec ? = 1/(3/5) = 5/3.
Frequently Asked Questions:
Q. What is the difference between cosine and secant?
A. Cosine is a trigonometric ratio that represents the ratio of the adjacent side to the hypotenuse of a right triangle. Secant is the reciprocal of cosine and represents the ratio of the hypotenuse to the adjacent side of a right triangle.
Q. How is the reciprocal of cosine used in real life?
A. The reciprocal of cosine is used in various fields such as engineering, architecture, surveying, and astronomy to calculate distances and heights.
Q. What is the value of sec 0 degrees?
A. The value of sec 0 degrees is 1/cos 0 degrees. Since cos 0 degrees = 1, sec 0 degrees = 1/1 = 1.