Trigonometric Ratios

Trigonometric ratios are ratios of the lengths of the sides of a right triangle. There are three main trigonometric ratios: sine, cosine, and tangent. These ratios are used to calculate angles in a right triangle. – Sine (sin): The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is calculated as sin(angle) = opposite/hypotenuse. – Cosine (cos): The cosine of an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is calculated as cos(angle) = adjacent/hypotenuse. – Tangent (tan): The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is calculated as tan(angle) = opposite/adjacent. For example, in a right triangle with an angle of 30 degrees, if the length of the side opposite the angle is 5 and the length of the hypotenuse is 10, you can calculate the sine of the angle as sin(30) = 5/10 = 0.5. One interesting fact about trigonometric ratios is that they are periodic functions, meaning they repeat their values at regular intervals. For example, the sine function repeats its values every 360 degrees. Overall, trigonometric ratios are essential in trigonometry for calculating angles and solving various problems involving right triangles.