Question

If cotA=5/4 and sinA<0, what is cscA?

Please show work/explain

Answer 1

Another way to write this problem would be as follows:

If tan A = 4/5 and the angle A is in the 3rd quadrant, what is csc A? In other words, what is sin A? If you can find sin A, then csc A = 1/sin A.

I'd really appreciate your showing or describing your own work. then I'd have something to which to respond.

Answer 2

Ok, so tanA is 5/4 I can construct a right triangle with the side opposite angle A being 5, the side adjacent being four, and the hypotenuse being the square root of 41. Since sin is negative sinA = -5/sqrt41, and cscA = -sqrt41/5.

Did I do this right?

Answer 3

thank you for sharing y our reasoning. I'll be right with you.

Answer 4

Looks great, except that cscA = -sqrt41/5. is open to misinterpretation. Suggest that you write -Sqrt(41)/5 so that it is obvious that the square root operator applies only to 41, not to 41/5. Nice work!

Answer 5

thank you!

Answer 6

Very happy to be of help!