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Gifs that you can stare at forever
By: davidavidson
 
Anonymous commenting is allowed
#46

simplescience (05/05/2013) [+] (5 replies)
The giant blue circle is known as the Unit Circle, which is used to find several aspects discussed in trigonometry, and has the formula x^2 + y^2 = 1. This can be used to find the radians, the angle of a hypothetical triangle within that circle, and then you can use the Pythagorean Theorem to find out any remaining aspects you wish to know.
The black line moving vertically demonstrates how you would get a triangle by using the unit circle if two sides are on an axis described above. One point is on one axis, while another point lies on the other axis. Connect the two and use Pythagorean Theorem to find the distance between the two axes or find the angles of the two remaining corners, although that takes a bit more work.
The black line moving horizontally shows you how to get a triangle within the unit circle if only one side is on the axis. This takes a bit more work, but can still be done, since you know one side and rework the Pythagorean Theorem to get the information you're looking for in terms of side length.
The red ellipses that go around the unit circle show the potential area of a triangle within the unit circle. The further out the red circle is, the greater are there is within a triangle at that point. If you're at the tip of the ellipsis, you've reached a point that has the greatest area for a triangle.
I could go on and on, but I figure you've all stopped reading by this point.
The black line moving vertically demonstrates how you would get a triangle by using the unit circle if two sides are on an axis described above. One point is on one axis, while another point lies on the other axis. Connect the two and use Pythagorean Theorem to find the distance between the two axes or find the angles of the two remaining corners, although that takes a bit more work.
The black line moving horizontally shows you how to get a triangle within the unit circle if only one side is on the axis. This takes a bit more work, but can still be done, since you know one side and rework the Pythagorean Theorem to get the information you're looking for in terms of side length.
The red ellipses that go around the unit circle show the potential area of a triangle within the unit circle. The further out the red circle is, the greater are there is within a triangle at that point. If you're at the tip of the ellipsis, you've reached a point that has the greatest area for a triangle.
I could go on and on, but I figure you've all stopped reading by this point.