Trigonometric functions are an essential part of pre-calculus and lay the foundation for advanced mathematical concepts. They help us understand the relationship between angles and sides in a right triangle. Let's dive into some key trigonometric functions: sine, cosine, and tangent.

Sine (sin): The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the hypotenuse of the triangle. For example, if we have a right triangle with an angle of 30 degrees and a hypotenuse of 10 units, the sine of the angle would be 1/2.

Cosine (cos): The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse. Using the previous example, if the adjacent side has a length of 8 units, the cosine of the angle would be 8/10 or 4/5.

Tangent (tan): The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. Using the same example, if the opposite side has a length of 5 units, the tangent of the angle would be 5/8.

Understanding these functions is crucial when working with trigonometry problems and applications. Practice using them in various scenarios to build your skills!