# Trigonometry

Trigonometry is a word derived from three Greek words - *Tri* meaning Three, *Gon* meaning Sides and *Metron* meaning to measure. Trigonometry is the study of relationships between the sides and angles of a triangle.

- Trigonometric Ratios
- Trigonometric Identities
- T-Ratios of Complementary Angles
- T-Ratios of Special Angles
- Angle of Elevation and Depression

### Advance Trigonometry

- Quadrants, Angles & Measurement
- Six Trigonometrical Ratios
- T-Ratios of Related Angles
- Properties of Trigonometric Functions

**Trigonometric Identities**

- Compound Angles: A + B and A − B
- Multiple Angle Identities
- Transformation of Product Into Sum or Difference
- Conditional Identities

**Trigonometric Equations**

- Trigonometrical Equations
- General Solutions of sin θ = 0, cos θ = 0, tan θ = 0
- General Solutions of sin θ = sin α, cos θ = cos α, tan θ = tan α
- Equation of the form: a cosθ + b sinθ = c

**Properties of Triangles**

- Sine Formula
- Napier’s Formula
- Cosine Formula
- Projection Formula
- Sub-multiple Half Angle Formula
- Triangle Area Formula
- Solution of Triangles

**Inverse Trigonometrical Functions**

- Inverse Trigonometrical Functions
- Properties of Principal Inverse Trigonometric Functions

### Trigonometric Ratios

If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.

- Sin A = a/c
- Cos A = b/c
- Tan A = a/b = Sin A/Cos A
- Cosec A = 1/Sin A
- Sec A = 1/Cos A
- Cot A = 1/Tan A

The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.

### T-Ratios of Important Angles

### Complementary Angles

sin (90° – A) = cos A, cos (90° – A) = sin A

tan (90° – A) = cot A, cot (90° – A) = tan A

sec (90° – A) = cosec A, cosec (90° – A) = sec A

### Standard Trigonometric Identities

Sin^{2}A + Cos^{2}A = 1

Sec^{2}A - Tan^{2}A = 1

Cosec^{2}A = 1 + Cot^{2}A

### Application of Trigonometry

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

- The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

- The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when you raise your head to look at the object.

- The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when you lower your head to look at the object.