Sin^-1 x – Detailed Explanation and Examples

The function $sin^{-1}x$, also known as the inverse sine function, is an inverse form of a trigonometric function, and theoretically, we call it a sine inverse “x” function. It can also be written as arc $sin(x)$ or can be read as arc of $sin(x)$ function. This function represents the inverse of the original sin(x) function. […]

Derivative of Tan^-1 x: Detailed Explanation and Examples

The derivative of $tan^{-1}x$ is equal to $dfrac{1}{1+x^{2}}$. Mathematically, the formula is written as $dfrac{d}{dx} tan ^{-1} x = (tan^{-1}x)^{‘} = dfrac{1}{1+x^{2}}$. We are basically differentiating the inverse function of a tangent with respect to the variable “$x$”. In this topic, we will study the derivative of the inverse of tan x and its proof […]

Double Angle Theorem – Identities, Proof, and Application

The double angle theorem is the result of finding what happens when the sum identities of sine, cosine, and tangent are applied to find the expressions for $sin (theta + theta)$, $cos (theta + theta)$, and $tan (theta + theta)$. The double angle theorem opens a wide range of applications involving trigonometric functions and identities. […]

Pythagorean Identities – Formula, Derivation, and Applications

The Pythagorean identities are important trigonometric identities that allow us to simplify trigonometric expressions, derive other trigonometric identities, and solve equations. Understanding these identities is essential when building a strong foundation to master trigonometric concepts and learn more advanced math topics. The Pythagorean identities are derived from the Pythagorean theorem. We use these identities to […]

Cosine Theorem – Explanation & Examples

The law of cosines or cosine theorem is a rule that provides us with the relation between the sides and angles of a triangle. The relationship is described using the formula: $c^2 = a^2 + b^2 -2abcos (z)$ or $c = sqrt{a^2 + b^2 -2abcos (z)}$, Read moreIs Trigonometry Hard?where $a$, $b$ and $c$ are […]