Math Question: Best way to learn the unit circle?

[Stroganoff]

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I took trig in high school five years ago and got through the unit circle section by basically memorizing the main parts and deriving the rest.

Now it's catching up to me in college...I'm pretty dependent on my calculator to tell me what sec (2 pi / 7) is for example.

Are there any methods to learning the unit circle once and for all?

 

[beep]

i tutor high school math...

draw the unit circle out on the same page as a sine plot, a cosine plot, and 30-60-90 and 45-45-90 triangles. study the sine and cosine values going back and forth between circle, plots, triangles. think of the unit circle as a condensed meta-version of the plots. get to the point where you can reproduce them all on a blank sheet of paper (it won't take long, really, once you really grasp the connections). if you really understand the conceptual links between them, the only thing you will need to memorize are the lengths of the triangle sides and sohcahtoa (actually, just sohcah).

oh, and forget memorizing tangent other than tan = sin/cos. you can always get it from the other values.

 

[Wiggy73]

Also remember the relationship between sine and cosine and the (x,y) coordinate of a point on the unit circle. The unit circle is a circle with radius 1 centered at the origin. Think of labeling each point on the circle by how many radians you have to go counterclockwise from the positive x-axis at (1,0) to get there. Then the sine of that many radians is the y coordinate of the point, and the cosine is the x coordinate. For example, it takes pi/2 radians to get to the top of the circle. Since the coordinates of that top point are (0,1), then cos(pi/2)=0 and sin(pi/2)=1.

 

[Stroganoff]

Thanks beep and Wiggy73. I'll have to try ths out.

beep, I just noticed we joined SDN the same day! And look what the Lounge did to my poor post count. 😀