What notation can you use to represent the inverse sine function? (Select all that apply.)
a) sin−1(x)
b) sin(x−1)
c) csc(x)
d) 1/(csc(x))
e) arcsin(x)
-1(x) or arcsin(x)
oops - that was sin-1(x)
The notations that can be used to represent the inverse sine function are:
a) sin^−1(x)
e) arcsin(x)
The notation commonly used to represent the inverse sine function is arcsin(x), so option e) is the correct answer.
To understand why arcsin(x) represents the inverse sine function, let's break down the notation:
- The function sin(x) represents the regular sine function. It takes an angle x and returns the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle with that angle.
- The inverse sine function, also known as arcsine function, is the opposite operation of the sine function. It takes a ratio value (x) and returns the angle whose sine is equal to that value.
So, to find the angle whose sine is x, you would use the notation arcsin(x).
Options a) (sin−1(x)) and b) (sin(x−1)) are incorrect because sin−1(x) could be misunderstood as the reciprocal of sin(x), and sin(x−1) represents the sine of the number one less than x.
Option c) (csc(x)) and d) (1/(csc(x))) are incorrect because csc(x) represents the cosecant function, which is the reciprocal of the sine function, not the inverse sine function.