Trigonometric ratios and identities are fundamental concepts in trigonometry. Trigonometry is the study of relationships between sides and angles of triangles. Trigonometric ratios and identities are used to solve problems related to triangles, especially right triangles.

HTML Bold tag: Trigonometric Ratios

Trigonometric ratios are the ratios of the sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent.

- Sine: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted by sin.
- Cosine: The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is denoted by cos.
- Tangent: The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is denoted by tan.

HTML Bold tag: Trigonometric Identities

Trigonometric identities are equations that are true for all values of the variables. There are many trigonometric identities, but some of the most common ones are:

- Pythagorean Identity: sin²θ + cos²θ = 1
- Reciprocal Identities:
- sinθ = 1/cscθ
- cosθ = 1/secθ
- tanθ = 1/cotθ
- Quotient Identity: tanθ = sinθ/cosθ
- Co-Function Identities:
- sin(π/2 - θ) = cosθ
- cos(π/2 - θ) = sinθ
- tan(π/2 - θ) = cotθ
- Even-Odd Identities:
- sin(-θ) = -sinθ
- cos(-θ) = cosθ
- tan(-θ) = -tanθ

HTML Bold tag: Applications of Trigonometric Ratios and Identities

Trigonometric ratios and identities have several practical applications, including:

- Navigation: Trigonometry is used in navigation to determine the direction and distance between two points.
- Engineering: Trigonometry is used in engineering to design and build structures such as bridges and buildings.
- Physics: Trigonometry is used in physics to calculate the motion of objects and the forces acting on them.
- Astronomy: Trigonometry is used in astronomy to calculate the positions and movements of celestial objects.
- Surveying: Trigonometry is used in surveying to determine the dimensions and layout of land.

In conclusion, trigonometric ratios and identities are essential concepts in trigonometry. They are used to solve problems related to triangles and have practical applications in various fields.