θ = ?
Hello. I am having difficulty with this problem:
Find the point on the terminal side of θ = -3pi/4 that has an x coordinate of -1
I was hoping that someone here would be able to help me out? I am actually trying to figure out what I am doing so if you could explain how you found the answer, I would really appreciate it. Thank you so much guys.
No, the sine of an angle will not return an angle. is a special angle for which you should know the trig. functions at that angle.
So, the -coordinate of the point is:
Recall we found hence:
And so, the point in question is (-1,-1). Try drawing a diagram, and you will easily see that the -coordinate has to be equal to the -coordinate, as the given angle lies along the line .
Well, it's a lot easier to memorize if you understand it. Imagine a right triangle having one angle of and one leg of length 1. Since , so that the other angle is also which means that the other leg also has length 1. By the Pythagorean theorem, the length of the hypotenuse is given by so that . That gives .