Determine an identity for cot 3θ.

[ZMS]

A) Determine an identity for cot 3θ. Must be in terms of sin θ and cos θ only.
B) Determine any restrictions on your identity over the interval 0≤θ≤2pi

I can do half of a, just confused on what cos 3θ a) an identity could be: Since cot 3θ is equal to cos 3θ/sin3θ, sin 3θ would be 3 sin 1.5θcos1.5θ. I'm just confused on what would cos 3θ be. I also don't get how to do b) at all. Can someone please help me with these questions. Thank you!

 

[tkhunny]

Please demonstrate your attempts. Have you considered that cot(3x) = cot(x + 2x)?

 

[ZMS]

Please demonstrate your attempts. Have you considered that cot(3x) = cot(x + 2x)?

So that means (cos 2x cos x - sin 2x sinx)/(sin 2x cos x + cos 2x sinx). Then, I used the double angle identities, but as much as I tried I keep getting stuck and far away from a simplified version.

 

[mmm4444bot]

There are some other identities for the cotangent function, on this list. :cool:

 

[Deleted member 4993]

So that means (cos 2x cos x - sin 2x sinx)/(sin 2x cos x + cos 2x sinx). Then, I used the double angle identities, but as much as I tried I keep getting stuck and far away from a simplified version.

Your problem statement did not specify that it needs to be simplified version. Just convert cos(2x) in terms of cos(x) and/or sin(x) - you'll be done.