(1) Reflexion in the x-axis: If \[P'\,\,(x',y')\]is the reflexion of the point \[P(x,y)\]on the x-axis, then the matrix \[\left[ \begin{matrix} 1 & 0 \\ 0 & -1 \\\end{matrix} \right]\] describes the reflexion of a point \[P(x,y)\]in the x-axis.
(2) Reflexion in the y-axis
Here the matrix is \[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\\end{matrix} \right]\]
(3) Reflexion through the origin
Here the matrix is \[\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\]
(4) Reflexion in the line \[\mathbf{y=x}\]
Here the matrix is \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
(5) Reflexion in the line \[\mathbf{y=}-\mathbf{x}\]
Here the matrix is \[\left[ \begin{matrix} \,\,0 & -1 \\ -1 & \,\,0 \\ \end{matrix} \right]\]
(6) Reflexion in \[y=x\,\mathbf{tan\theta }\]
Here matrix is \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin
more...
\[\sin \theta =\frac{\text{Perpendicular}}{\text{Hypotenues}}=\frac{y}{r}\]
\[\frac{2n\pi \pm A}{2}\]
\[\tan \theta =\frac{\text{Perpendicular}}{\text{Base}}=\frac{y}{x}\]
\[\cot \theta =\frac{\text{Base}}{\text{Perpendicular}}=\frac{x}{y}\]
\[\sec \theta =\frac{\text{Hypotenues}}{\text{Base}}=\frac{r}{x}\]
\[\text{cosec}\theta =\frac{\text{Hypotenues}}{\text{Perpendicular}}=\frac{r}{y}\]
(1) Relation between trigonometric ratios (functions)
(i) \[\frac{\sqrt{4-\sqrt{2}-\sqrt{6}}}{2\sqrt{2}}\]
(ii) \[\tan \theta .\cot \theta =1\]
(iii) \[\cos \theta .\sec \theta =1\]
(iv) \[\tan \frac{A}{2}\] (v) \[\cot \theta =\frac{\cos \theta }{\sin \theta }\]
(2) Fundamental trigonometric identities
(i) \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1\]
(ii) \[1+{{\tan }^{2}}\theta ={{\sec }^{2}}\theta \]
(iii) \[1+{{\cot }^{2}}\theta =\text{cose}{{\text{c}}^{2}}\theta \]
(3) Sign of trigonometrical ratios or functions : Their signs depends on the quadrant in which the terminal side of the
