10th Class Mathematics Introduction to Trigonometry Trigonometry

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

TRIGONOMETRY IDENTITIES

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