Question

Use a graph of the function to approximate the solution of the equation on the interval
[−2π, 2π].
(List the solutions in increasing order from left to right on the x-axis. Round your answers to three decimal places.) cot x = −1

Answer 1

cot π/4 = 1

now, where is cot(x) negative? Use π/4 as your reference angle.

Answer 2

cot 7π/4 = -1
but how do i get to the other answers?

Answer 3

oh, come on. You want QII and QIV. So, using π/4 as a reference angle, that gives you for your first solution, 3π/4

Now the period of cot(x) is π, so add/subtract π over and over till you arrive at -2π or 2π

3π/4+π/4 = 7π/4

3π/4-π = -π/4
-π/4 - π = -5π/4

So, your solutions are

-5π/4, -π/4, 3π/4, 7π/4

Did you draw your triangles? It almost always makes things easier to visualize.