Question

If cos(x)=4/5 and sin(x)<0, find cot(x)

Answer 1

Recall that \[\large \cos x=\frac{adjacent}{hypotenuse}\]Since we have,\[\large \cos x=\frac{4}{5}\]We can label our sides accordingly.

Answer 2

We can solve for the missing side using the Pythagorean Theorem.

Answer 3

\[\large 4^2+(opposite)^2=5^2\]Solving for the opposite side reveals that it's length is 3.
Do you understand this part ok? :)

Answer 4

Yeah, I think I've got it! Thanks so much!

Answer 5

cot(x)= 4/3, right?

Answer 6

So to solve for cot x, we recall our relationship for that,\[\large \cot x=\frac{adjacent}{opposite}\]They informed us that the sin x < 0. Meaning we should have gotten a -3 for that length.

It would have been more approapriate to draw it in the coordinate plane maybe, so we could see that the triangle is in the 4th quadrant.

Answer 7

\[\large \cot x=\frac{\cos x}{\sin x} \quad =\quad \frac{\frac{4}{5}}{-\frac{3}{5}}\]This is another way you could do it if you remember this identity for cotangent.
I put the negative on the sine term since they told us it was negative at the start.

Hope I didn't confuse you more :C

Answer 8

Oh I see! Nope, I understand. Thanks!

Answer 9

Np c:

Answer 10

So, just to make sure, cot(x)=-4/3, right?

Answer 11

Yup looks good! :D

Answer 12

Awesome! You rock!