Trigonometry is an essential branch of mathematics that deals with the relationships between angles and sides of triangles. It is especially useful in solving problems involving right triangles. In this lesson, we will explore the basic concepts of trigonometry including the sine, cosine, and tangent functions.

To understand trigonometry, it is important to know how to label the sides of a right triangle. The side opposite the right angle is called the hypotenuse, while the other two sides are known as the adjacent and opposite sides. Let's consider a right triangle with an angle θ:

The sine of angle θ (sinθ) is defined as the ratio of the opposite side to the hypotenuse, cosine (cosθ) is the ratio of the adjacent side to the hypotenuse, and tangent (tanθ) is the ratio of the opposite side to the adjacent side.

Now, let's take a look at a few examples to better understand how to apply trigonometry:

Example 1: Find the value of sinθ if the opposite side length is 5 and the hypotenuse length is 13.

Using the formula sinθ = opposite/hypotenuse, we plug in the values to get:

sinθ = 5/13.

Example 2: Given that cosθ = 3/5, find the length of the adjacent side if the hypotenuse length is 5.

Using the formula cosθ = adjacent/hypotenuse, we can substitute the given values to obtain:

3/5 = adjacent/5. Solving for adjacent, we get:

adjacent = 3.

Example 3: If tanθ = 4/3, find the length of the opposite side when the adjacent side is 3.

Using the formula tanθ = opposite/adjacent, we substitute the values to find:

4/3 = opposite/3. Solving for the opposite side, we get:

opposite = 4.

Remember to practice using these trigonometric functions to become more comfortable with applying them. Trigonometry is a powerful tool widely used in various fields such as engineering, physics, and computer graphics. So, keep up the hard work and enjoy exploring the fascinating world of trigonometry!

Remember, math is fun!