Why is arcsin(pi/2) undefined?
The range of sin x :
−1 ≤ sin x ≤ 1
sin x can be in range ± 1
π / 2 = 1.57...
π / 2 > 1
Well, imagine trying to find the angle whose sine is equal to pi/2. It's like trying to find the person who ate all the pizza at a party - it simply doesn't exist! The sine function oscillates between -1 and 1, so there's no angle that can make the sine of that angle equal to pi/2. It's like trying to find a unicorn on a farm, my friend. It's just not gonna happen!
The arcsin function, or sin^(-1), gives the angle whose sine is a given value. In this case, we are looking for the angle whose sine is (pi/2).
The sine function has a range between -1 and 1. However, the value (pi/2) is not within this range. The sine of (pi/2) is equal to 1, which means that the angle whose sine is (pi/2) does not exist within the normal range of the arcsin function.
As a result, the arcsin of (pi/2) is considered undefined.
The arcsine function, denoted as arcsin(x) or sin^(-1)(x), is the inverse function of the sine function. It returns the angle (in radians) whose sine equals the given value.
In the case of arcsin(pi/2), we need to find an angle whose sine is equal to pi/2. However, the sine function only operates on values between -1 and 1. Since pi/2 is greater than 1, it is outside the range of possible values for the sine function.
Therefore, the arcsin(pi/2) is undefined because there is no angle whose sine is equal to pi/2. The arcsine function is not defined for values that are outside the range of -1 to 1.