Find the point on the terminal side of θ = -3π/4 that has an x coordinate of -1. Show your work, please

Step-by-step explanation:

is the same as -135°. Since positive angles are measured counterclockwise, and this one is negative, we are measured clockwise. Doing that puts us into the second quadrant where both x and y are negative. The terminal side of the angle is the side that is free to move and open and close the angles. The initial side is the one that is on the positive x-axis and does not move. We are looking for a point on the terminal side of that angle, which means we are looking for the (x, y) coordinate on that point where x = -1.

Now...between the negative x-axis and the terminal side of the angle is a 45°. That's what's important here. From the origin we move left along the negative x-axis to -1. From that point we can drop an altitude to meet the terminal side and have created a right triangle in the process.  Where the altitude meets the terminal side is the point (-1, y) that we are looking for.

Now comes the point in your work where you need to remember the Pythagorean triple for a 45-45-90 triangle. On a unit circle, everything is based on 1 unit, and the side length across from a 45 degree angle is 1. In our case, because we are in the second quadrant, both the side lengths across from both of those angles will be 1 and they will both be negative. That means that the point on the terminal side of that angle is (-1, -1).