# Writing cotangent in terms of cosinehow?

1. Feb 1, 2010

### megr_ftw

1. The problem statement, all variables and given/known data
How can I write cos(x) in terms of cot(x)? I tried using the pythagorean identities and fundamental identities but still cannot figure it out.
The answer must start as the following: cosine(x)=.....

2. Relevant equations
All the trig identies. I think it wants me to use the fundamental ones but Im not sure thats possible
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

3. The attempt at a solution
I know that cotangent=cos/sin but I need it to only be in terms of cosine which seems impossible to me because I've tried everything. Also, I do believe it is okay to use cot^2(x) with the pythagorean identities.

2. Feb 1, 2010

### Staff: Mentor

Which do you want to do - write cos(x) in terms of cot(x), or cot(x) in terms of cos(x)? Your title and problem statement are at odds. Assuming it's the latter,
cot(x) = cos(x)/sin(x), and sin2(x) = 1 - cos2(x), hence sin(x) = +/-sqrt(1 - cos2(x)).

3. Feb 1, 2010

### megr_ftw

I want to express cosine in terms of cotangent. Cosine is y and cotangent is x, so I want to express y in terms of x
sounds confusing which is why I am having trouble with it

4. Feb 1, 2010

### Staff: Mentor

cos(x) = [cos(x)/sin(x)]*sin(x) = cot(x)*sin(x) = cot(x) * 1/csc(x)

Now use the identity that cot2(x) = 1 - csc2(x), solving for csc2(x) first, and then csc(x). Use that to replace 1/csc(x) in the formula above. That will give you cos(x) in terms of cot(x).

5. Feb 1, 2010

### megr_ftw

i thought 1/csc is equal to sin? and 1/sec= cos. and cosine is what im trying to use.

6. Feb 1, 2010

### megr_ftw

oh and i see how you may be confused, the title of the thread is wrong. sorry

i need cosine in terms of cotangent

7. Feb 1, 2010

### Mentallic

Yes but Mark is telling you to use an identity that involves csc(x) and cot(x). See if you can complete where he was leading you.