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.
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.
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?
$\displaystyle cot\theta= \frac{1}{tan\theta}$
$\displaystyle tan\theta= \frac{sin\theta}{cos\theta}$
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?