Explain why arcsin 3 is undefined.
look at the graph of y = sinx
It has a range between -1 and +1
since 3 is outside that range ......
The arcsin function, denoted as arcsin(x) or sin^(-1)(x), is the inverse function of the sine function. It gives you the angle whose sine is equal to x, within a certain domain.
The sine function has a range between -1 and 1. However, the arcsin function has a domain between -1 and 1, while its range can be any real number between -π/2 and π/2. This means that the input value of arcsin(x) must be within the range of -1 and 1 to have a defined output.
In this case, you mentioned arcsin(3), but the domain of arcsin(x) is limited to values between -1 and 1. Since 3 is greater than 1, it is outside the valid domain for the arcsin function. Hence, arcsin(3) is undefined.
The arcsine function, denoted as arcsin(x) or sin^(-1)(x), is the inverse function of the sine function. It gives you the angle whose sine is equal to the given value.
Now, the sine function, sin(x), is defined for all real numbers between -1 and 1. Its output values range from -1 to 1.
However, when we take the arcsine function, the input values must lie within the range -1 to 1. This is because the arcsine function "undoes" the sine function; it gives you back the angle whose sine is equal to the given value.
In this case, we are trying to find the arcsine of 3, which is outside the range of -1 to 1. Therefore, it is undefined. There is no angle that has a sine equal to 3.
To check this using a calculator or trigonometric tables, you would need to look for the range of output values for the arcsine function. You would see that it is not defined for inputs greater than 1 or less than -1. Hence, when you enter arcsin(3) into a calculator, it will most likely return an error or give an undefined result.