Trigonometric Functions

Trigonometric functions are mathematical functions that relate angles of a right triangle to the lengths of its sides. The main trigonometric functions are sine (sin), cosine (cos), and tangent (tan). To calculate angles using trigonometry, you can use the definitions of the trigonometric functions. For example, if you know the lengths of two sides of a right triangle, you can use the sine function to find the angle opposite the given side. Similarly, you can use the cosine function to find the angle adjacent to the given side, and the tangent function to find the angle opposite to the given side divided by the angle adjacent to it. One important fact to remember is that in a right triangle, the sum of the angles is always 90 degrees. This property is known as the Pythagorean theorem. For example, if we have a right triangle with a hypotenuse of length 5 and an opposite side of length 3, we can use the sine function to find the angle opposite the side: sin(angle) = opposite/hypotenuse sin(angle) = 3/5 angle = sin^(-1)(3/5) angle ≈ 36.87 degrees This is just one way to calculate angles using trigonometry. There are many other applications and formulas that can be used to solve various trigonometric problems.