Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles. It is used to solve problems involving measurements and calculations in fields such as engineering, physics, and astronomy.
The three main trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle, and are used to find missing side lengths or angles.
Trigonometry has numerous real-life applications, such as in navigation, architecture, surveying, and engineering. It is also used in fields such as physics, astronomy, and even music and art.
The Pythagorean Theorem is a fundamental concept in trigonometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In equation form, it is written as a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate system. It is used in trigonometry to relate the coordinates of a point on the circle to the sine and cosine values of the corresponding angle. This allows for easy calculation of trigonometric functions for any angle, not just those within a right triangle.