# 10th Class Mathematics Introduction to Trigonometry Trigonometry

Trigonometry

Category : 10th Class

TRIGONOMETRY

FUNDAMENTALS

• Trigonometry is the study of relationship between the sides and angles of a triangle.

Trigonometrical ratio

• Trigonometric ratio of angle in a right angled AABC are defined as follows:

$\sin \theta =\frac{AB}{AC}=\frac{P}{h}$

$Cos\theta =\frac{AB}{AC}=\frac{b}{h}$

$\tan \theta =\frac{AB}{AC}=\frac{p}{b}$

The ratio $\text{cosec}\theta ,\,\text{sec}\theta$ and $\cot \theta$ are respectively the reciprocals of the $sin\theta ,cos\theta$and $tan\theta .$

i.e., $\text{sin}\,\theta =\frac{1}{\text{cosec}\,\theta },\text{cos}\theta =\frac{1}{\sec \theta }\text{and}\,\,\text{tan}\,\theta =\frac{1}{\cot \theta }$

Trigonometric ratio of some specific angles

 $\angle \theta$ ${{0}^{o}}$ ${{30}^{o}}$ ${{45}^{o}}$ ${{60}^{o}}$ ${{90}^{o}}$ $\sin \theta$ 0 $\frac{1}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{\sqrt{3}}{2}$ 1 $\cos \theta$ 1 $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$ 0 $\tan \theta$ 0 $\frac{1}{\sqrt{3}}$ 1 $\sqrt{3}$ Not defined $\cos ec\theta$ Not defined 2 $\sqrt{2}$ 2 1 $\sec \theta$ 1 $\frac{2}{\sqrt{3}}$ $\sqrt{2}$ 2 Not defined $\cot \theta$ Not defined $\sqrt{3}$ 1 $\frac{1}{\sqrt{3}}$ 0
• ${{\sin }^{2}}\theta +co{{s}^{2}}\theta =1$
• $se{{c}^{2}}\theta -ta{{n}^{2}}\theta =1$
• $cose{{c}^{2}}\theta -co{{t}^{2}}\theta =1$
• $\sin \left( {{90}^{{}^\circ }}-\theta \right)=cos\theta ;\,\,cos\left( {{90}^{{}^\circ }}-\theta \right)=sin\theta$
• $sec\left( {{90}^{{}^\circ }}-\theta \right)=cosec\theta ;\,\,cosec\left( {{90}^{{}^\circ }}-\theta \right)=sec\theta$
• $tan\left( {{90}^{{}^\circ }}-\theta \right)=cot\theta ;\,\,cot\left( {{90}^{{}^\circ }}-\theta \right)=tan\theta$

##### Notes - Trigonometry

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