3 ms·
That's incorrect, you have to choose the proper inverse branch if you want the answer to be 9.
by measurablefunc 1y ago
That's incorrect, you have to choose the proper inverse branch if you want the answer to be 9.
- madars 1y agoThere is no choice here - each inverse is uniquely determined. That's similar to how 3 and -3 are both square roots of 9 (i.e., solutions to x^2=9), but sqrt(9)=3 as it denotes the principal square root, which by convention is always the non-negative value. Of course, in a different context we might design functions to have multi-valued properties, like atan2(x,y) != atan(y/x) in general (atan2 takes quadrant in account and returns full range [-pi, pi], atan only returns principal values in [-pi/2, pi/2]) as practical applications benefit from preserving quadrant beyond just the principal inverse (or not failing when x=0!)
- measurablefunc 1y agoThe inverse branches are not unique, you might think there is no choice being made but picking the standard branch is a choice b/c I can always shift the result by 2π by picking a different branch of the inverse. The answer is not unique & the assumption is that the calculators are using the standard branch.
- madars 1y agoOf course, but the choice is standard and thus the answer is 9. I can define a non-standard sqrt(x) which sometimes gives the positive root and sometimes the negative one, and then sqrt(sqrt(16)) could be -2 or undefined (if I defined sqrt(16)=-4) but that's just silly - the only reasonable interpretation for what the calculator should show for sqrt(sqrt(16)) is simply 2.
- saagarjha 1y agoYes, that's what those functions do.
- deruta 1y agoI was with you until I remembered the default unit for angles in calculators is degrees, not radians.
- gs17 1y agoThe page also specifies it's degrees mode.