The reciprocal of the tangent function.
Trigonometric Functions: Cotangent is one of the six basic trigonometric functions, including sine, cosine, tangent, cosecant, and secant.
Definitions and Terminologies: Basic definitions and terminologies related to angles, triangles, degrees, and radians used in trigonometry.
Unit Circle: Graphical representation of the values of the six basic trigonometric functions on a circle with a radius of one.
Trigonometric Ratios: Comparison of the ratios of the sides of a right-angled triangle to its angles.
Properties of Cotangent: Properties and characteristics of the cotangent function, such as range, domain, period, and period symmetry.
Graphs and Transformations: Techniques to plot and transform the cotangent function graph and understand its behavior.
Identities and Equations: Manipulating trigonometric equations and identities involving cotangent and other trigonometric functions.
Inverse Trigonometric Functions: Inverse trigonometric functions such as arc-cotangent can be used to solve problems involving cotangent.
Applications: Examples of applications of cotangent function in real-life problems such as engineering, physics, and astronomy.
Trigonometric Algebra: Applying algebraic techniques to solve trigonometric equations, inequalities, and identities.
Calculus with Cotangent: Derivatives, integrals, and advanced calculus topics related to cotangent function.
Basic definition: The cotangent function is defined as the ratio of the adjacent side to the opposite side in a right-angled triangle.
Periodicity: The cotangent function is periodic with a period of π, that is, cot(x + π) = cot(x).
Sign function: The cotangent function changes sign at every π/2 interval, that is, cot(x + kπ) has a sign different from cot(x) for any integer k.
Graphical representation: The graph of the cotangent function consists of vertical asymptotes at every odd multiple of π/2 and horizontal asymptotes at every even multiple of π.
Inverse cotangent: The inverse cotangent function or arccot(x) is defined as the angle whose cotangent is x. The range of arccot(x) is (0, π) or (−π/2, π/2) depending on the convention used.
Other related functions: The cotangent function is related to other trigonometric functions such as sine and cosine through the identities cot(x) = cos(x)/sin(x) and cot(x) = 1/tan(x), where tan(x) is the tangent function.