Which of the following statements best describes the domain of the functions sine and arcsin?
A)Sine domain is all real numbers; Arcsin domain is all real numbers.
B)Sine domain is restricted; Arcsin domain is all real numbers.
C)Sine domain is all real numbers; Arcsin domain is restricted.
D)Sine domain is restricted; Arcsin domain is restricted.
y = sin x
what values can x have?
any real number right?
y = sin^-1 x
what values can x have?
Only between -1 and + 1 right?
To determine the domain of a function, we need to consider the values that the input, or independent variable, can take.
For the sine function (sin), the input is an angle, typically measured in radians. The domain of the sine function is all real numbers since an angle can take any real value.
On the other hand, for the arcsine function (arcsin), the input is a ratio or value between -1 and 1 that represents the sine of an angle. The output of the arcsine function is an angle. Therefore, the domain of the arcsine function is restricted to values between -1 and 1 because the input must be a valid sine ratio to obtain a meaningful angle as the output.
So, the correct statement that best describes the domain of the sine and arcsine functions is:
C) Sine domain is all real numbers; Arcsin domain is restricted.