Final answer:
The correct equation is arccsc(x) = arcsin(1/x), as it represents the inverse relationship between the cosecant and sine functions, indicating that arccsc(x) finds the angle whose sine is the reciprocal of x.
Step-by-step explanation:
The correct equation related to arcsecant is arccsc(x) = arcsin(1/x). The arcsecant function, arccsc(x), is the inverse of the cosecant function, csc(x), which is the reciprocal of the sine function, sin(x). Therefore, arccsc(x) is used to find the angle whose cosecant is x. Since csc(x) = 1/sin(x), taking the inverse of both sides, we get arccsc(1/sin(x)) = x. By further manipulation, we can say that arccsc(x) = arcsin(1/x) because we are essentially finding the angle whose sine is the reciprocal of x.
The equation arccsc(x) = 1/sin(x) suggests a relationship between arccsc and the sine function directly, but this would imply that arccsc(x) gives us the value of 1/sin(x), which is not the case. The correct interpretation is that arccsc finds the angle whose cosecant (which is 1/sin(x)) is x, hence the equation arccsc(x) = arcsin(1/x).