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Find all solutions of the equation in the interval [0,2pi). Write your answer in terms of pi.
√3 cot(theta)1=0
I got cot(theta)= pi/3, but the identity of cotangent is x/y, so I'm not sure where to look at. Is the answer just pi/3?
 9 months ago
 9 months ago
Find all solutions of the equation in the interval [0,2pi). Write your answer in terms of pi. √3 cot(theta)1=0 I got cot(theta)= pi/3, but the identity of cotangent is x/y, so I'm not sure where to look at. Is the answer just pi/3?
 9 months ago
 9 months ago

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hartnnBest ResponseYou've already chosen the best response.1
did you mean you got thetha = pi/3 ?
 9 months ago

NoelGrecoBest ResponseYou've already chosen the best response.0
That's one answer, but there is another angle on that interval where the cotangent is positive and the reference angle is also pi/3.
 9 months ago

jkl3inbergBest ResponseYou've already chosen the best response.1
Yes hartnn, and NoelGreco the only place there's a reference angle of pi/3 is 1/2 and root3/2, are those my answers?
 9 months ago

hartnnBest ResponseYou've already chosen the best response.1
he meant there are 2 solutions you got cot theta =1/ sqrt 3 right ? there are 2 angles in [0,2pi) which satisfies this, one angle is pi/3 which you got it correct and other will be (pi/3 +pi) =... ? because cot function is periodic in pi
 9 months ago

jkl3inbergBest ResponseYou've already chosen the best response.1
I got 1/sqrt 3 yes, but that needs to be rationalized to root 3 / 3, right? Which I don't see anywhere on the unit circle
 9 months ago

hartnnBest ResponseYou've already chosen the best response.1
oh, you are using unit circle, ok then cot = cos / sin search for the values where the ratio of cos/ sin would equal 1/sqrt 3 one when cos = 1/2 and sin = sqrt 3 /2 and one more when cos =1/2 and sin = sqrt 3/2 those 2 angles will be your solution
 9 months ago

jkl3inbergBest ResponseYou've already chosen the best response.1
so pi/3 and 4pi/3, thanks. I get these kinds of problems but cot=x/y really confused me. How exactly did you end up with 1/2 and root3/2?
 9 months ago

hartnnBest ResponseYou've already chosen the best response.1
ok, cot (theta) = 1/ sqrt 3 is the ratio of cos and sine functions so, for sin and cos the standard values are 1/2 and sqrt 3/2 for the standard angle pi/3, (we need to remember standard angles and their values or we can use the unit circle) ratio of only these would give us 1/sqrt 3...thats how.
 9 months ago

jkl3inbergBest ResponseYou've already chosen the best response.1
Ok, got it. Thanks!
 9 months ago
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