The Siddhanta Shiromani is a treatise on astronomy and mathematics that was written by Bhaskara II in 1150. It is divided into four parts, the first of which is devoted to calculus.

The Circle Area Theorem states that the area of a circle is equal to $\pi r^2$, where $\pi$ is the ratio of a circle's circumference to its diameter and $r$ is the radius of the circle.

The Power Rule states that the derivative of $x^n$ is $nx^{n-1}$, where $n$ is a real number.

The Fundamental Theorem of Calculus states that the integral of a function $f(x)$ from $a$ to $b$ is equal to $F(b) - F(a)$, where $F(x)$ is the antiderivative of $f(x)$.

The Sine Function is defined as the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

The Cosine Function is defined as the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse.

The Tangent Function is defined as the ratio of the length of the opposite side of a right triangle to the length of the adjacent side.

The Cotangent Function is defined as the ratio of the length of the adjacent side of a right triangle to the length of the opposite side.

$\sin 30^\circ = \frac{1}{2}$

$\cos 45^\circ = \frac{\sqrt{2}}{2}$

$\tan 60^\circ = \sqrt{3}$

$\cot 30^\circ = \sqrt{3}$

$\sin^{-1} \frac{1}{2} = 30^\circ$

$\cos^{-1} \frac{\sqrt{2}}{2} = 45^\circ$

$\tan^{-1} \sqrt{3} = 60^\circ$