(sin 210°)^(sin 210°) I was just playing with my calc until I put in this math and it showed math error. Based on HS math it should be -0.5^-0.5= -1.414 which isn't... I am not sure if there is any other concept that is not taught to us. Can anyone help?

It needs to be done in radians. Works fine in that case, since sin210 is ~0.7π. You can then convert it back to degrees with: 180/π x 0.7π ~= 40 degrees As for why it doesn't work in degrees, I have no idea. I know there are lots of formulas that only work in radians - which is why radians exist in the first place, but no idea why this should be one of them.

sin(210 deg)^sin(210 deg) = - 1.41421356 i This is what google calculator says... An imaginary number??? Any math professors here?

I'm confused: (-1/2)^(-1/2) = 1/((-1/2)^(1/2)) = 1/ √(-1/2) = 1/((1/√2)i) So unless you are allowing imaginary numbers you will get an error

Imaginary numbers aren't degree level math lmao, I'm still sleepy and just woke up hence my taking my sweet time to figure it out but basically you're taking the square root of a negative number (power 1/2 = sqrroot) so you end up with 2sqrt(-0.5) which is an imaginary number.

That’s one reason why 0, 1, pi, e and i are considered the five important numbers in math because many times they hold math concepts in place (e^(i*pi)+1=0). You can’t always treat them like you could any other number. For example, if you treated 0 like you would any other number, you could actually mathematically prove the Orwellian concept that 2+2=5 (weird stuff happens when you divide by 0, which is why it doesn’t happen). similar situation with taking the even roots of negative numbers.

Did your calc is on the good settings ? Because depending on the settings, the result are not the same.