Inverse Trigonometric Functions

Inverse Trigonometric Functions are functions that allow us to find the angle that corresponds to a given trigonometric ratio. In other words, they help us find the angle when we know the value of a trigonometric function such as sine, cosine, or tangent. For example, if we are given the value of sin(θ) = 0.5, we can use the inverse sine function (sin^-1) to find the angle θ that corresponds to this sine value. In this case, sin^-1(0.5) = 30 degrees, which means that the angle θ is 30 degrees. Similarly, if we are given the value of cos(θ) = -0.5, we can use the inverse cosine function (cos^-1) to find the angle θ that corresponds to this cosine value. In this case, cos^-1(-0.5) = 120 degrees, which means that the angle θ is 120 degrees. One important fact to note is that the range of inverse trigonometric functions is limited to certain intervals in order to make them one-to-one functions. For example, the range of sin^-1(x) is -π/2 ≤ sin^-1(x) ≤ π/2, while the range of cos^-1(x) is 0 ≤ cos^-1(x) ≤ π. Overall, inverse trigonometric functions are essential tools in trigonometry for finding angles based on trigonometric ratios, and they play a crucial role in solving various mathematical problems involving angles and trigonometric functions.