Introduction to trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. In this tutorial, we will introduce the basics of trigonometry, including the definitions of the six trigonometric functions and how to use them to solve problems involving triangles.

The six trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are defined in terms of the sides and angles of a right triangle, which is a triangle with one 90-degree angle. The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

To use the trigonometric functions to solve problems involving triangles, we first need to identify which sides and angles are known and which are unknown. Then, we can use the definitions of the trigonometric functions to set up equations and solve for the unknown values. For example, if we know the length of the opposite side and the hypotenuse of a right triangle, we can use the sine function to find the measure of the angle.

In this tutorial, we will go over these concepts in more detail and practice using the trigonometric functions to solve problems involving triangles. We will also learn about the inverse trigonometric functions, which are used to find the angle measures when the side lengths are known. By the end of this tutorial, you should have a good understanding of the basics of trigonometry and be able to apply these concepts to solve problems involving triangles.