Help finding Theta in the unit circle

[psycho]

I'm stuck on another problem.

Problem 8 b):
http://www.math.poly.edu/courses/ma1024 ... -09-21.pdf

I've already started working at the problem and got an answer but don't know if it's correct.

1) I drew a line straight down from (x,y) to the x-axis.
2) I made the length from the bottom of the line to the origin -1/2.
3) I realized that this was a unit circle, with radius 1 on all sides, so I made the bolded line length 1.
4) I created a triangle with hypoteneus 1, and two lengths of 1/2.
5) In the triangle, I saw a right angle with the X-axis and noticed that if both lengths are 1/2, the two remaining angles must be equal.
6) I then had a right triangle with angles 45-45-90 degrees.
7) I set up this equation and solved for x:

180-x=45
x=135 degrees

Could you please check my work? Thanks so much for your help!

 

[psycho]

I worked on the problem some more and realized that you can't assume that both lengths are even; you only know the length from the origin to the bottom of the line (which is 1/2).

I set up this equation instead:
cos a=(1/2)/1
cos^-1(1/2)=60 degrees

180-60=120 degrees

 

[stapel]

Please post the questions here, so we don't have to go looking for them. Thank you.

In the accompanying diagram of a unit circle, the ordered pair (x; y) [in the second quadrant] represents
the point where the terminal side of [the angle theta] intersects the unit circle. If x = -1/2, what is one possible value for theta?

Eliz.