Contents

**Introduction to Trigonometry**

__Trigonometry__

The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). In fact, **trigonometry **is the study of relationships between the sides and angles of a triangle.

- Find height of tall building or tower without actually measuring it
- Find the height at which an object , airplane or balloon is flying
- Find the distance of a vehicle or ship from a tower.
- Used extensively in the field of construction.

__Trigonometric Ratios__

**Using this logic ,In right ΔABC**

**sine of ∠ A = P/H = BC/AC**

**cosine of ∠ A = B/H = AB/AC**

**Numerical**: In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine : sin A, cos A ,sin C, cos C.

__Trigonometric Ratios of Some Specific Angles__

**Numerical**: In Δ ABC, right-angled at B, AB = 5 cm and ∠ ACB = 30°. Determine the lengths of the sides BC and AC.

**Solution**:

Tan C =P/B =AB/BC

Or Tan 300 = 5cm/BC

1/√3 = 5cm /BC (using table, tan 300 =1/√3).

Or BC = 5√3 cm.

Now we can find the third side by Pythagoras Theorem. We can also find third side using trigonometric identities.

Sin C = P/H = AB/AC

Or Sin 300 = 5cm/AC

Or 1/2 = 5cm /AC (using table, Sin 300 =1/2).

Or AC = 10 cm.

__Trigonometric Ratios of Complimentary Angles__

**Memory tip:**

**Numerical:**Evaluate tan 65°/ cot 25°

__Trigonometric Identities__

sin2 A + cos2 A = 1,

sec2 A – tan2 A = 1 for 0° ≤ A < 90°,

cosec2 A = 1 + cot2 A for 0° < A ≤ 90°.

**Numerical**: Express the ratios cos A, tan A and sec A in terms of sin A.

**Solution**: cos2 A + sin2 A = 1,

Or cos2 A = 1 – sin2 A, i.e., cos A = ±√ 1 − sin2 A

or cos A = √1 − sin2 A (Ignoring the negative value , since sin A is positive, Cos A will also be positive.)

tan A = sin A/cos A = sin A/√1 − sin2 A

sec A = 1/cosA = 1/√1 − sin2 A

**Also Read :**

### MATHS Revision Notes

**Chapter:01 Real Numbers System****Chapter:02 Polynomials****Chapter:03 Pair of Linear Equations in Two Variables****Chapter:04 Quadratic Equation ****Chapter:05 Arithemetic Progressions****Chapter:06 Triangles****Chapter:07 Coordinate Geometry****Chapter:08 Introduction to Trignometry****Chapter:09 Some Application Of Trignometry****Chapter:10 Circles****Chapter:11 Constructions****Chapter:12 Area Related to Cirles****Chapter:13 Surface Area Volume****Chapter:14 Stastistics****Chapter:15 Probability**