10th Class Mathematics Introduction to Trigonometry Trigonometry

Trigonometry

Category : 10th Class

TRIGONOMETRY

FUNDAMENTALS

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

TRIGONOMETRY RATIO

• Trigonometrically ratio of angle in a right angle $\Delta ABC$ are defined as follows

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

$cos\theta =\frac{BC}{AC}=\frac{b}{h}$

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

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

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

Trigonometric ratio of some specific angles

 $\angle \theta$ ${{0}^{{}^\circ }}$ ${{30}^{{}^\circ }}$ ${{45}^{{}^\circ }}$ ${{60}^{{}^\circ }}$ ${{90}^{{}^\circ }}$ $\sin \theta$ 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 $\sqrt{2}$ $\frac{2}{\sqrt{3}}$ 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

TRIGONOMETRY IDENTITIES

• ${{\sin }^{2}}\theta +co{{s}^{2}}\theta =1$
• $se{{c}^{2}}\theta -ta{{n}^{2}}\theta =1$
• $cose{{c}^{2}}\theta -co{{t}^{2}}\theta =1$
• $Sin\left( {{90}^{{}^\circ }}-\theta \right)=cos\theta \text{ }cos\text{ }\left( {{90}^{{}^\circ }}-\theta \right)=sin\theta$
• $sec\left( {{90}^{{}^\circ }}-\theta \right)=cosec\theta \text{ }cosec\text{ }\left( {{90}^{{}^\circ }}-\theta \right)=sec\theta$
• $tan\left( {{90}^{{}^\circ }}-\theta \right)=cot\theta \text{ }cot\left( {{90}^{{}^\circ }}-\theta \right)=tan\theta$

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