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
cot π/4 = 1
now, where is cot(x) negative? Use π/4 as your reference angle.
cot 7π/4 = -1
but how do i get to the other answers?
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.
To approximate the solution of the equation cot(x) = -1 on the interval [-2π, 2π], we can use a graph of the cotangent function.
First, let's plot the graph of the cotangent function. The cotangent function is the reciprocal of the tangent function, so we can find the values of cot(x) by finding the values of tan(x) and taking their reciprocals.
Next, we need to find the points on the graph where cot(x) is equal to -1. These points represent the solutions to the equation cot(x) = -1.
Looking at the graph, we can see that the cotangent function crosses the line y = -1 at multiple points within the interval [-2π, 2π]. We need to find the x-coordinates for these points.
To approximate the solutions, we can look for the x-values where the graph intersects the line y = -1. Start from the leftmost point where the graph crosses the line and move to the right, noting the x-values where the intersections occur.
Once we've identified the x-values of the intersections, we should round them to three decimal places and list them in increasing order from left to right on the x-axis.
Note: The cotangent function has a period of π, so the solutions to the equation cot(x) = -1 repeat after every π units.
Hope this helps! Let me know if you have any further questions.