Point value on Unit Circle

[Lokito]

Directions: Sketch and find the coordinates of the point corresponding to each angle on the unit circle.
5. S is at 225 degrees. T is at 270 degrees. U is at 330 degrees.

T is easy to find because it lies on a maximum, but I missed class when the method for finding unit circle values without a calculator was discussed. The other two, S and U, can be found using something about the properties of right angles, but I don't know how to do it. The back of the book lists the decimal approximation, which I can find myself, but that's not the answer the teacher is looking for, because it's a calculator answer. Help?

 

[tkhunny]

You simply must add a few angles' exact values to your memory.

0º

sin(0º) = 0
cos(0º) = 1

30º

sin(30º) = 1/2
cos(30º) = sqrt(3)/2

45º

sin(45º) = cos(45º) = sqrt(2)/2

60º

cos(60º) = 1/2
sin(60º) = sqrt(3)/2
Notice how nicely this relates to the results for 30º

90º

sin(90º) = 1
cos(90º) = 0
Notice how nicely this relates to the results for 0º

With these in your pocket, you can solve all those you have presented with the slight additional consderation of Quadrant. There is a concept known as the "Reference Angle" You should learn what this is. I will just hint at it.

225º is a lot like 45º, since 180º + 45º = 225º. It's just 45º under the negative x-axis, rather than 45º above the positive x-axis.

270º is a lot like 90º. It's just in the negative y-direction, rather than the positive y-direction.

330º is a lit like 30º, since 360º - 30º = 330º. It's just 30º under the x-axis, rather than 30º above the x-axis.

Let's see if this gets you anywhere.