Question

If θ is an angle in standard position and its terminal side passes through the point (-7,-5), find the exact value of cot ⁡ θ cotθ in simplest radical form.

Answer 1

Plot the point (-7, -5). We are in quadrant 3.

We also know that tan θ = opp/adj.

Cot θ = adj/opp.

Let us use a^2 + b^2 = r^2 to show you how to find r, the radius aka hypotenuse.

Look: (-7)^2 + (-5)^2 = r^2

If you should ever need to find r, do this:

(-7)^2 + (-5)^2 = r^2

(49) + 25) = r^2

74 = r^2

Take the square root on both sides of the equation to find r.

sqrt{74} = sqrt{r^2}

sqrt{74} = r

It is ok to simplify the sqrt{74} but not needed.

We now have the three sides of the triangle that is form in quadrant 3.

We can now read cot θ from the triangle itself.

So, cot θ = adj/opp = (-7)/(-5) or 7/5.

No need to find r but I simply wanted to show you how it's done in case you are given a question where r must be found.