## Trigonometric Functions

Preliminaries We were introduced to the trigonometric functions in class $latex {XI}&s=1$ with their general definitions for any angle $latex {\theta}&s=1$. The specialty of these functions is that their values get repeated after an interval. This is because after every interval of $latex {2 \pi^c}&s=1$, the angles have same initial and terminal arms. Basics :… Continue reading Trigonometric Functions

Posted in XII

## Linear Programming Problems

Linear Programming is a technique of obtaining optimum solution to a problem out of many solutions. It has a specific objective such as maximizing profit or minimizing the expenses. This technique is typically applied to solve decision making problems in business; but its origin is in WWII. It was developed to make the best (optimum) use… Continue reading Linear Programming Problems

Posted in XII

## Matrices III

Inverse of a Matrix Unlike numbers, the division operation is not defined for matrices. A similar (but not same) operation is to find the inverse of a matrix. Note that only square matrices can have inverses. When a square matrix $latex A$ is non-singular ($latex |A| \ne 0$), its inverse exists ($latex = A^{-1}$) and is… Continue reading Matrices III

## Three Dimensional Coordinate Geometry II

Lines A line is uniquely specified, when coordinates of 2 distinct points are known. In other words, only 1 line passes through 2 distinct points. Let $latex P (x_1,y_1,z_1)$ and $latex Q(x_2,y_2,z_2)$ be those 2 points.   Let $latex R(x,y,z)$ be any point on that line. Then, $latex {\vec {PR} = t (\vec {PQ})}&s=2$ since… Continue reading Three Dimensional Coordinate Geometry II