Lecture

Trigonometric Functions: Arctan and Arccot

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Description

This lecture covers the definitions and properties of the arctan and arccot functions, including their graphs and notable values. It explains the relationship between these functions and their respective trigonometric counterparts, as well as how to restrict them to specific intervals. The instructor emphasizes the importance of understanding the inverse trigonometric functions and provides insights into their graphical representations. The lecture concludes with a discussion on the graphs of arctan and arccot functions, highlighting key takeaways and preparing students for practical examples.

In MOOC

Trigonometric, Logarithmic and Exponential Functions

This course provides the fundamental knowledge related to these functions. It is structured around 9 chapters spread over 12 weeks: The angle and its measurement Trigonometric functions sine and cosine and their inverses Trigonometric functions tangent and cotangent and their inverses Trigonometric formulas (addition, bisection, etc.) Harmonic oscillations Trigonometric equations Triangle relations (sine and cosine theorems) Continuity and derivability of trigonometric functions Logarithmic and exponential

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Related concepts (30)

Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

Trigonometry

Trigonometry () is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

Atan2

In computing and mathematics, the function atan2 is the 2-argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number The function first appeared in the programming language Fortran in 1961. It was originally intended to return a correct and unambiguous value for the angle θ in converting from Cartesian coordinates (x, y) to polar coordinates (r, θ).

List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.

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