Inverse of Cosine Function

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 Graph

The graph of cosine function resembles the graph of sine function with a basic difference that for x = 0 sin function graph passes from the origin while at x = 0, the cosine function graph passes from (0, 1) at y-aixs. Following is the graph of the value of cosine function i.e. y = cos x...

Cos in Unit Circle

Cosine Function can be defined using unit circle. Let’s understand how we can define cosine function in terms of unit circle....

Inverse of Cosine Function

The inverse of a cosine function known as arc-cosine function and abbreviated as arccos(x) or cos-1(x) is defined as follows...

Hyperbolic Cosine Function

Hyperbolic Functions are analog equivalent of Trigonometric Function whose algebraic expression is in the terms of exponential function. The hyperbolic cosine function abbreviated as cosh(x) where x is a hyperbolic angle is a concept of hyperbolic geometry. Like (cos(x), sin(x)) represents a point on a unit circle, (cosh(x), sinh(x)) represents a point on a unit hyperbola i.e., xy = 1 where sinh(x) represents hyperbolic sine function. The algebraic expansion of hyperbolic cos function is given as...

Cosine Function in Calculus

The branch of calculus in mathematics deals with the differentiation and integration of a given function. Differentiation of function is the rate of change in the function with respect to the independent variable while integration is the reverse process of differentiation that deals with finding the integral of a function whose derivative exist....

Sine and Cosine Functions

Following graph represents the key difference between both sine and cosine function:...

Cos Value Table

Following table provides the values of cosine function for some common angles in the first quadrant of cartesian plane –...

Cos Function Identities

The basic trigonometric identities related to cosine function is mentioned below:...

Solved Examples on Cosine Function

Here are some solved examples to help you better understand the concept of cosine function....

Practice Questions: Cos Functions

Q1. What is the formula to calculate the cos of an angle in a right-angled triangle?...

Summary – Cosine Function

The cosine function, denoted as cos(x), is a fundamental trigonometric function defined as the ratio of the base to the hypotenuse in a right-angled triangle and is essential across various fields like physics, engineering, and geometry due to its periodic nature, which is instrumental in modeling wave behaviors. It has a domain of all real numbers and a range from -1 to 1, repeating its cycle every 2π radians or 360 degrees, evident from its wave-like graph that starts at (0,1). In terms of calculus, the derivative of cos(x) is − sin(x), and its integral yields sin(x)+C, with C as the constant of integration. This function also extends to hyperbolic forms, such as cosh(x), enhancing its application in various mathematical contexts and solutions, including wave calculations and oscillations in physical systems....

Cosine Function: FAQs

1. What is Cosine Function?...