|
|
|
|
|
|
|
On calculator: why does 1/sin give an answer different fr...
|
|
by
Dr.Robert
|
|
|
|
On calculator: why does 1/sin give an answer different from s^-1. Aren't the two identical?
|
|
|
|
|
|
Responses
|
|
|
Good question. Hopefully do remember that sin-1x is not the same thing as 1/sin x. The two distinct meanings of superscript -1 are well known i.e. exponentiation to the power of -1 and other the inverse function – e.g. if f:[0, ∞) -> R is given by f(x) = x2, f-1(x) = √x not equals 1/x2= f(x)-1. In the case of sin-1 x, it means the latter, not the former. Also depends on which calculator set up has been used.
Especially for trigonometric functions, an exponent in the same place will mean different things depending on whether it is positive or negative. When the exponent is positive, it refers to taking the appropriate multiplicative power. To example, sin2 x = (sin x)2 = (sin x) * (sin x). However, when the exponent is -1, it always refers to the inverse function, not the multiplicative inverse. Therefore, sin-1 (x) = arcsin x not equals csc x = 1/sin x = (sin x)-1. |
|
|
|
|
by
Winpossible
|
|
Sep 05, 10 10:07PM PST
|
|
|
|
|
|
Thank you. Appreciate the feedback. You rule!
|
|
by
RobertG
|
|
Sep 05, 10 10:33PM PST
|
|
|
|
|
|
|
|
|
|
|
|
|
|