Find all values of θ in the interval [0, 2pi], given:

cot θ = -1/√3

cosθ= 1/2

I don't really need the answer, just need to know how to solve this type of problem :(

I greatly appreciate your answer :)

Thank you.

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- Mar 16th 2013, 07:02 PMBlast1309Find all values of θ in the interval [0, 2pi]
Find all values of θ in the interval [0, 2pi], given:

cot θ = -1/√3

cosθ= 1/2

I don't really need the answer, just need to know how to solve this type of problem :(

I greatly appreciate your answer :)

Thank you. - Mar 16th 2013, 07:18 PMProve ItRe: Find all values of θ in the interval [0, 2pi]
First, it helps to write the functions in terms of sine, cosine or tangent. Once you have done that, make note of whether your function is positive or negative, take note of which quadrants that function is positive or negative in. Work out the focus angle (for the first quadrant) and then adjust according to whichever quadrants you need to be in.

See how you go. - Mar 16th 2013, 07:29 PMBlast1309Re: Find all values of θ in the interval [0, 2pi]
- Mar 16th 2013, 07:35 PMProve ItRe: Find all values of θ in the interval [0, 2pi]
Well in your first equation, like I said, put it as either a sine, cosine, or tangent equation. The equation is equivalent to $\displaystyle \displaystyle \tan{(\theta)} = -\sqrt{3} $.

In which quadrants is the tangent function negative? - Mar 16th 2013, 07:37 PMShakarriRe: Find all values of θ in the interval [0, 2pi]
$\displaystyle cot\theta= \frac{1}{tan\theta}$

$\displaystyle tan\theta= \frac{sin\theta}{cos\theta}$

Therefore

$\displaystyle cot\theta= \frac{cos\theta}{sin\theta}$

You know that

$\displaystyle \frac{cos\theta}{sin\theta}=\frac{-1}{\sqrt{3}}$

And

$\displaystyle cos\theta= \frac{1}{2}$

Can you solve these two equations for theta? - Mar 16th 2013, 09:12 PMBlast1309Re: Find all values of θ in the interval [0, 2pi]
- Mar 16th 2013, 09:15 PMProve ItRe: Find all values of θ in the interval [0, 2pi]
Now you need to try to find ALL solutions in the given region. Like I said, think about which quadrants you need to be in...