trig Function, reference angle

[mathmarauder]

I am not understanding how my textbook came up with this.
Because the reference angle is 60 degrees we know that r is 2, x =1 and y = - radical 3
another example
Because the reference angle is pi/4 or 45 degrees , we know the r= radical 2 , x =-1 and y = -1.

can you tell me how they came up with that?
im trying to evaluate the trig function (without a calculator)
but i cant get past this step, because i dont know where they got the r value as well
as the x and y.
like what would be the r,x and y value for
pi/4 or 90 degrees?

 

[Loren]

Are you familiar with the "unit circle"? On the rectangular coordinate system graph, with the origin as the center draw a circle with radius of one unit. From a point in quadrant I on the circle, draw a line segment to the Origin and draw another line segment perpendicular to the x-axis. You now have a right triangle. Label the acute angle (at the origin) of the right triangle "theta". Label the point P(x,y). Now, position P such that theta = 60°. You know that the hypotenuse, r, is 1 unit in length. You should be able to figure out that the measure of x is 1/2 unit and the measure of y is ?3. You can determine these measures by realizing that if you have an equilateral triangle, all angles are 60°. If you draw the altitude of the equilateral triangle, you divide it into two right triangles having angles of 30-60 and 90 degrees. You can see that the short leg is one-half the length of a side and all sides of the equilateral triangle are of one unit. Using the Pythagorean Theorem, you can determine that if the hypotenuse is 1, the long leg is ?3.
Does that help?

 

[mathmarauder]

Thank you for the help