Answer:
The terminology for the inverse sine function, "arcsin," is derived from its mathematical meaning. To understand this terminology, let's break it down:
Sine Function (sin): The sine function, denoted as "sin," is a trigonometric function that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In simpler terms, it gives you the sine value of an angle in a right triangle.
Inverse Function: The "arc" in "arcsin" signifies that it's an inverse function. In mathematics, an inverse function undoes the operation of the original function. So, while the sine function takes an angle and gives you its sine value, the inverse sine function takes a sine value and gives you the angle (in radians) that corresponds to that sine value.
"sin" is short for "sine": The abbreviation "sin" is short for "sine." So, "arcsin" can be interpreted as "the inverse of sine" or "the function that finds the angle whose sine is a given value."
In summary, "arcsin" is a concise way to describe the inverse sine function, which allows you to find the angle (in radians) whose sine is a specified value. It is a standard notation in trigonometry and mathematics, helping to express this concept efficiently.