How do I solve Cot(ArcSin (-12/13))?

Draw a triangle:

arcsin gives the angle, so draw a right triangle with one of the base angles labeled as y.

So now we know:

sin(y) = -12/13 <-- this actually isn't sufficient since we don't know if the x or y is negative, only that one of them is.

That tells us that the opposite side (to the y) is 12 (really negative 12), then the hypotenuse is 13. Now you can find the other leg:

13² - 12² = 169 - 144 = 25

-->

other leg is √25 = 5

Therefore the cotangent (adjacent over hypotenuse) is:

5/12

OK, now the tricky part...I said earlier that the -12 could be either the opposite or the hypotenuse...well actually that's incorrect, the hypotenuse can NEVER be negative...therefore we KNOW that the opposite should be -12, which means the cotangent should be:

5/-12 = -5/12

Edit:

Actually, you don't know if the adjacent side is negative or not, so the answer should be:

±5/12

Edit:

Here's a picture that hopefully will help:

http://i961.photobucket.com/albums/ae91/jbennatt/Y...

ArcSin(-12/13) = -67.38

Cotx = (tanx)^-1 so…

cot(-67.36) = -0.417

REMEMBER:

ArcSin, ArcCos, ArcTan will help you solve her an angle.

cotx, cscx, secx are the inverses of the tanx, sinx and cosx respectively.

Arc Sin