# Posts for Tag: HSC

### Differentiation Formulas – HSC Math

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. if $y=f(x)$ is a function, then its first derivative, i.e. ${\dy}/{\dx}=f'(x)=\lim↙{h→0}{f(x+h)-f(x)}/h$ GeneralRead More

### Functions – HSC Math

A function is a special relationship where each input has a single output. It is often written as $y=f(x)$ where $x$ is input and $y$ is the output value. Say $x_1,x_2∈D$ $f(x_1)=f(x_2)$ if $x_1=x_2$ or, $f(x_1)≠f(x_2)$ if $x_1≠x_2$ then the function is called a one-to-one function. Where D is the set of decimal numbers. ifRead More

### Trigonometric Properties of a Triangle – HSC Math

Sine Rule $a/{Sin\ A}=b/{Sin\ B}=c/{Sin\ C}$ Cos Rule $cos\ A={b^2+c^2-a^2}/{2bc}$ $cos\ B={a^2+c^2-b^2}/{2ac}$ $cos\ C={a^2+b^2-c^2}/{2ab}$ $a=b\ cos\ C+c\ cos\ B$ $b=c\ cos\ A+a\ cos\ C$ $c=a\ cos\ B+b\ cos\ A$ Tan Rule $tan\ {B-C}/2={b-c}/{b+c}\ cot\ A/2$ $tan\ {A-B}/2={a-b}/{a+b}\ cot\ C/2$ $tan\ {C-A}/2={c-a}/{c+a}\ cot\ B/2$ $tan\ A/2=√{(s-b)(s-c)}/√{s(s-a)}={(s-b)(s-c)}/{∆}$ $tan\ B/2=√{(s-a)(s-c)}/√{s(s-c)}={(s-a)(s-c)}/{∆}$ $tan\ C/2=√{(s-a)(s-b)}/√{s(s-c)}={(s-a)(s-b)}/{∆}$ Here, $s={a+b+c}/2, ∆=$Area of that triangle.Read More

### Matrix and Determinant Formulas – HSC Math

Let A is a matrix with m row and n column. Then the dimension of a matrix A is m x n. Let A and B are matrices with dimension m x n and p x q respectively. Then multiplication of A and B, i.e. A.B is possible if and only if n=p. if \$A=[\tableRead More