Trigonometric ratios are derived from right triangles, which are triangles with one 90-degree angle. These ratios help relate the angles of a triangle to the lengths of its sides. Here’s a simple explanation:### 1. Right Triangle BasicsA right triangle has three sides:- Hypotenuse: The longest side, opposite the right angle.- Adjacent Side: The side next to the angle you’re focusing on, but not the hypotenuse.- Opposite Side: The side across from the angle you’re focusing on.### 2. Trigonometric RatiosThere are three main trigonometric ratios: Sine, Cosine, and Tangent. These ratios are based on the relationships between the angles and the sides of the triangle.- Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the hypotenuse.sin(theta) = frac{text{Opposite}}{text{Hypotenuse}}- Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse.cos(theta) = frac{text{Adjacent}}{text{Hypotenuse}}- Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the adjacent side.tan(theta) = frac{text{Opposite}}{text{Adjacent}}### 3. How These Ratios Are DerivedThe trigonometric ratios are derived by examining different right triangles with the same angles but different side lengths.