Introduction to Trigonometry

Trigonometry is a branch of mathematics that deals with the study of angles and the relationships between the lengths of the sides of triangles. It has applications in various fields such as physics, engineering, and astronomy.

Basic Trigonometric Ratios

The three basic trigonometric ratios are sine, cosine, and tangent, often abbreviated as sin, cos, and tan. These ratios are defined for acute angles in a right-angled triangle.

• Sine (sin θ): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
• Cosine (cos θ): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
• Tangent (tan θ): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Trigonometric Functions

Trigonometric functions are functions of an angle used to relate the angles of a triangle to the lengths of its sides. The main trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.

Trigonometric Identities

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the variables. Some common trigonometric identities include the Pythagorean identities, cofunction identities, and reciprocal identities.

Applications of Trigonometry

Trigonometry has wide-ranging applications in real-world problems such as calculating distances, angles of elevation, navigation, and analyzing periodic phenomena like sound and light waves.

Practice Problems

1. Find the value of sin(60°).

2. Calculate the value of cos(45°).

3. Solve for the unknown side in a right-angled triangle using trigonometric ratios.

Remember to review the definitions, formulas, and practice problems to solidify your understanding of trigonometry!