A branch of mathematics which deals with the relationships between the sides and angles of a right triangle.
Basic Concepts: Introduction to trigonometry, definitions of sine, cosine, tangent, reciprocal functions, ratios, and formulas.
Trigonometric Ratios: Understanding the ratios between sides of a right triangle, calculations, and use of table values.
Fundamental Formulas: Basic principles and formulas like Pythagoras theorem, Quadratic equation, Angular measure, and Radians.
Trigonometric Identities: Derivations and applications of cos^2x + sin^2x = 1, sin (90 - x) = cos x, and many more.
Angles of Elevation and Depression: Concept of directing angles, horizontal distance, angle of elevation, and depression, examples, and applications.
Solving Triangles: Calculation of unknown angles or sides in right-angled triangles using trigonometric ratios.
Graphs of Trigonometric Functions: Understanding and plotting graphs of sine, cosine, tangent, reciprocal functions, and their properties.
Inverse Trigonometric Functions: Definition and use of arcsine, arccosine, and arctangent functions.
Trigonometric Equations: Solving equations involving trigonometric functions like sin x = 1/2, cos x = 2/3, and many more.
Applications of Trigonometry: Applications to real-life situations like navigation, engineering, surveying, astronomy, and optics.
Pythagorean Triangles: These are right triangles where the sides are in rational numbers. Such as 3-4-5, 5-12-13, 8-15-17.
30-60-90 Triangles: In this type of triangle, the angles are in the ratio of 30:60:90. The longest side is twice of the smallest side. The most common example of this type is the 1-√3-2 triangle.
45-45-90 Triangles: Here, the two acute angles are in the ratio of 45:45 whereas, the hypotenuse is √2 times of one shorter side. The most common example of this type is the 1-1-√2 triangle.
Special Angle Triangles: These triangles have acute angles that correspond to the special angles (30, 45, 60 degrees) of a regular right triangle. They can be expressed in radical or integer forms. Examples include 7-24-25, 35-44-51, 37-48-55.
Integer Triangles: These are right triangles where all three sides are integers. Some examples are 5-12-13, 7-24-25, and 8-15-17.
Non-Integer Triangles: These are right triangles where at least one side is not an integer. These triangles often require the use of trigonometric functions to solve.
Oblique Triangles: These are triangles that do not have a right angle. The trigonometric functions still apply to these triangles, but different formulas need to be used to solve them.