Question

If cot=2/5, sen<0, how much is cos?

Answer 1

So adyacent is 2, and the hip is sqrt of 29, right?

Answer 2

sen?

Answer 3

sin

Answer 4

sine*

Answer 5

OK, if sine is negative, what quadrent is it in?

Answer 6

3 or 4, right?

Answer 7

OK. So, it is in 3 or 4. Now, where could the cotangent be positive?

Answer 8

oh...in 4

Answer 9

Cotangent positive in 4? Ummm....

Answer 10

cot is adjacent/opposite...so adjacent should be positive...right?

Answer 11

oh...but sine is negative...so the opposite is negative, so adjacent needs to be negative!

Answer 12

This question seems to be using the unit circle definition.
\(\cot\theta=\dfrac{\cos\theta}{\sin\theta}\) So for that to be positive, both the sine and cosine must have the same sign.

Answer 13

Ok. everything is understood until there

Answer 14

Have you done anything with the unit circle yet?

Answer 15

"oh...but sine is negative...so the opposite is negative, so adjacent needs to be negative!"

And that IS correct.

Answer 16

See, there is a way to equate a right triangle to the unit circle... but not sure if you are using that.

Answer 17

I have done it a long time ago, I know how to measure the trigonometric functions of a respective angle using the 45 triangles and the 90-60-30 triangles

Answer 18

Yep, we've done that before

Answer 19

OK, so, what do you think the answer would have to be then?

Answer 20

Well, then we would need to measure the hypotenuse...sqrt of 29

Answer 21

and then cos should be 2/sqrt29 ...but that's not a choice

Answer 22

negative

Answer 23

oh...then I multiply by sqrt of 29/sqrt of 29 and I get the answer :D

Answer 24

Negative :P

Answer 25

Ah, yah, you had to rationalize the denominator.

Answer 26

Yep :) forgot about that :P

Answer 27

Thanks a lot

Answer 28

np. Have fun!