| Trigonometrical Function | Domain | more...
In the right angled triangle \[OMP,\] we have base \[=OM=x,\] perpendicular \[=PM=y\] and hypotenuse \[=OP=r\]. We define the following trigonometric ratio which are also known as trigonometric function.
\[\sin \theta =\frac{\text{Perpendicular}}{\text{Hypotenues}}=\frac{y}{r}\]
\[\frac{2n\pi \pm A}{2}\]
\[\tan \theta =\frac{\text{Perpendicular}}{\text{Base}}=\frac{y}{x}\]
\[\cot \theta =\frac{\text{Base}}{\text{Perpendicular}}=\frac{x}{y}\]
\[\sec \theta =\frac{\text{Hypotenues}}{\text{Base}}=\frac{r}{x}\]
\[\text{cosec}\theta =\frac{\text{Hypotenues}}{\text{Perpendicular}}=\frac{r}{y}\]
(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 more...
Two angles are said to be allied when their sum or difference is either zero or a multiple of \[{{90}^{o}}\].
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