**trignomentry**** :**

In a right-angled\( \triangle\) OAB, where \(\angle \mathrm{BOA}\)=\(\mathrm{\theta}\)

- \(\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{O B}\)
- \(\cos \theta=\frac{\text { Base }}{\text { Hypotenuse }}=\frac{O A}{O B};\)
- \(\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}=\frac{A B}{O A};\)
- \(\csc \theta=\frac{1}{\sin \theta}=\frac{O B}{A B}\);
- \(\sec \theta=\frac{1}{\cos \theta}=\frac{O B}{O A}\)

**Trigonometrical Identities:**

- \(\sin ^{2} \theta+\cos ^{2} \theta=1\)
- \(1+\tan ^{2} \theta=\sec ^{2} \theta\)
- \(1+\cot ^{2} \theta=\csc ^{2} \theta\)

Value of T rotations

**Angle**** of Elevation:**

Suppose a man from a point O looks **up** at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O is called the angle of elevation of P as seen from O.

\(\therefore\)The angle of elevation of P from O= \(\angle \mathrm{AOP}\)

**An angle of Depression:**

Suppose a man from a point O looks **down** at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O is called the angle of depression of P as seen from O.