Answer:
Explanation:
The function sin^-1, also known as arcsine, is the inverse function of the sine function sin(x). This means that if y = sin(x), then x = sin^-1(y).
However, it is important to note that sin^-1 is only the inverse function of sin for a restricted domain. Specifically, sin^-1 only returns values between -π/2 and π/2 radians, or -90° and 90° in degrees. This is because sin(x) is an odd function, which means it has symmetry about the origin and therefore has multiple x-values for a given y-value.
In the case of sin(3π/4), this value is equal to √2/2. Using a calculator or trigonometric table, we can find that sin^-1(√2/2) = π/4, which is not equal to 3π/4.
The reason why sin^-1(sin(3π/4)) ≠ 3π/4 is because 3π/4 is not within the restricted domain of sin^-1. Instead, we must find the angle between -π/2 and π/2 that has a sine value of √2/2. This angle is π/4, as mentioned above.
Therefore, while sin^-1 and sin are inverse functions, we must be careful to consider the restricted domain of sin^-1 when using these functions together.