What is the Cosine Function?
Cosine Function is a trigonometric function which is basically periodic in nature. Cosine Function is expressed as cos x where x is one of the acute angles of a right-angled triangle. Cosine Function finds the ratio of base and hypotenuse for a given value of x. The cosine function is abbreviated as the cos(x) or cos(θ) where x is the angle in radians and theta θ is the angle in degrees generally. The cosine function can be defined using a unit circle i.e., a circle of unit radius as we will see later in this article. It is periodic in nature and repeats its values after every complete rotation of angles. On a cartesian plane, it can be referred to as the vector component of the hypotenuse parallel to the x-axis.
Cosine Function Definition
The cosine function is defined in a right-angled triangle as the ratio of the length of the side adjacent to the concerned angle to the length of the hypotenuse. Mathematically Cosine Function is given as
Cos x = Cos θ = Length of Base/Length of Hypotenuse = b/h = OB/OA
where x is the angle in radians and θ is the equivalent angle in degrees.
Domain and Range of Cos Function
We know that for a function, domain is the permissible input values and range is the output value for that particular input or domain value. Hence, we can assume that function acts like a processor which takes input, processes it and gives particular output. The domain and range of cos function is discussed below:
- Domain of cosine function: R i.e., set of all real numbers.
- Range of cosine function: [-1, 1], i.e., output varies between all real numbers between -1 and 1.
Period of a Cosine Function
The function is periodic in nature, i.e., it repeats itself after 2π or 360°. In other words, it repeats itself after every complete rotation. Hence, the period of cosine function is a complete rotation or an angle of 360° (or 2π).
Reciprocal of a cosine function
The reciprocal of a cosine function is known as secant function or sec for short. Mathematically, the reciprocal of cosine function is given as
sec(θ) = 1/cos(θ)
As per rules of Reciprocals, if we multiply the Cos x with Sec x the product will be always 1.
Cosine Function
the Cosine function or the cos function in short is one of the six Trigonometric Functions fundamental to trigonometry. Cosine in Trigonometry is given as the ratio of the base to the hypotenuse of a right-angled triangle. Cosine Function is represented as Cos x where x is the angle for which the cosine ratio is calculated. In terms of function, we can say that x is the input or the domain of the cosine function.
It is extensively used in a wide range of subjects like Physics, Geometry, and Engineering among others generally by leveraging its periodic nature. For example, it is used to define the wave nature of sound waves, calculations of electric flux through a plane surface, etc. In this article, we learn in detail about what is cosine function, the domain and range of the cosine function, the period, and the graph of the cosine function.
Table of Content
- What is the Cosine Function?
- Cos in Unit Circle
- Cosine Function Graph
- Inverse of cosine function
- Cosine Function in Calculus
- Cos Function Identities