Unit Circle Stuff

The Wikipedia entry related to the Unit Circle.

Khan Academy instructional video about expanding from the SOH CAH TOA definition of trig functions as ratios of a right triangle to finding trig values for all angles.

This page does not have any videos, but it has some good information and some very nice interactive tools. Two good ones. Under "Try It Yourself": (1) interactive tool where you can move the point on the circle and see how the Trig values change (draws the sides and tangent on the associated right triangle), and (2) just underneath the interactive tool is the "Interactive Unit Circle." By clicking on it, you are taken to another unit circle to trace around, but now you can see how the coordinates influence the graphs of sine, cosine, and tangent.

An online math lesson from mathwarehouse.com, which includes interactive demonstrations and practice.

Here are two free PDF files you can download. The first has a completely filled-in unit circle including angles in degrees and radians and the coordinates. The second file is a blank unit circle.

This site includes flashcards and games related to converting given angles from degrees to radians (or vice versa). A good practice tool if having issues with the angles.

This site includes an interactive tool. You are given a value to calculate. You drag a terminal side around the side of the circle until you reach the angle, and then use the given coordinates to find the particular trigonometric value.

This links to a flash animation created by dudefree.com. Is intended to help students by allowing as much or as little information as the user wants. Also includes a quiz mode.

One of the main ways to find values on the unit circle is the hand trick. This video uses pictures to try and explain.

This video explains the points on the unit circle using the x and y distances (longest, middle, shortest) to decide which coordinate goes where. A thorough explanation.

This video starts by dividing up the circle into pieces to show where the various radian angles are located. Next, he uses a 1-2-3 trick along with symmetry to fill in the rest of the values.

A way, through song, to help remember some of the values. Warning: song is annoying.

The constant pi is equal to (circumference) / (diameter) of any circle. That means 2pi is the circumference of the unit circle (r = 1) and the base distance we use for radian measure. However, some are calling for a new math constant, called tau, which would be (circumference) / (radius). That would make the circumference of the unit circle 1tau, which would make dividing the unit circle into fractions of 1 tau rather than fractions of 2pi. This video is a pro / con discussion about which way would be better.

Any Twitter comments including the words "unit circle" are displayed here. Interesting to see student and teacher reactions.

A Sunday cartoon from Summer 2015 involving the Unit Circle and "tan". It sometimes helps to add some humor to the class.

If you understand the unit circle and the values, you can at least appreciate the cleverness of the pick-up line. Forget the quality.