Question

given cos x =-2/5 and cot x >0 find csc x, sin x, tan x, cot x

Answer 1

So, this is probably best approached as a logical problem. cos x = -2/5 will correspond to two angles. One of which will have yield a positive sin x, and the other will yield a negative sin x.

After you find this, you just need to use the definitions of the other functions to find their values.

Answer 2

Thanks, but based on the fact that the cot is >0, then we have one angle in quadrant 3. I got the answers cscx= \[-5\sqrt{21}/21\], sinx= \[-\sqrt{21}/5\], tanx=\[-\sqrt{21}/2\], and \[-2\sqrt{21}/21\]but the teacher marked all my signs wrong which I don't understand as in the third quadrant both sin and cos are negative

Answer 3

Since Cot x > 0 and cos x is negative, sin x has to be negative as well, meaning csc x will be negative, tan x will be positive, and cot x will be positive.

Answer 4

Do you see why that is?

Answer 5

yes, that is what I thought and your answer matches mine above... but the teacher marked it wrong and took points off my exam... thanks for your help!

Answer 6

I put the teacher's answers above... mine were correct...

Answer 7

Very interesting. Even teachers make mistakes, try talking to him/her!