Table of Contents
Introduction to Trigonometry
Trigonometry is the mathematics of angles and triangles. It is a powerful tool for solving problems in physics, engineering, and other sciences. Trigonometry can be used to find distances between points, to find angles in a triangle, and to solve problems involving circles.
Trigonometric Ratios
There are six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant.
The sine ratio is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine ratio is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent ratio is the ratio of the length of the opposite side to the length of the adjacent side. The cotangent ratio is the ratio of the length of the hypotenuse to the length of the adjacent side. The secant ratio is the ratio of the length of the hypotenuse to the length of the opposite side. The cosecant ratio is the ratio of the length of the hypotenuse to the length of the adjacent side.
Basic Identities of Sine and Cosine
1. The sine and cosine functions are both periodic, with a period of 2π.
2. The sine and cosine functions are both orthogonal, meaning that their product is zero.
3. The sine and cosine functions are both inverse functions of each other.
4. The sine and cosine functions are both continuous functions.
Double and Triple Angles
When two angles are combined to form a new angle, the result is called a “double angle.” The measure of a double angle is the sum of the two original angles.
For instance, if two angles have measures of 30 and 45 degrees, the measure of the double angle is 75 degrees.
If three angles are combined to form a new angle, the result is called a “triple angle.” The measure of a triple angle is the sum of the three original angles.
For instance, if three angles have measures of 30, 45, and 60 degrees, the measure of the triple angle is 135 degrees.
Sum and Difference of Angles
The sum of two angles is the sum of the measures of the angles.
The difference of two angles is the difference of the measures of the angles.
Values of Trigonometric Ratios at Various Angles:
The following table lists the values of the trigonometric ratios at various angles.
The Six Main Functions of an Angle that are Commonly Used in Trigonometry are:
1. Angle of Elevation
2. Angle of Depression
3. Angle of Inclination
4. Angle of Incidence
5. Angle of Reflection
6. Angle of Refraction
Know more about:
1. Inverse Trigonometric Functions
2. Inverse Trigonometric Functions in Maths
3. Important Topic of Maths: Trigonometric Equation
