The Unit Circle--the Cosign, Sign, and Tangent Functions

[jiacinto]

Can someone explain the unit circle to me and what those formulas are? I never could get it.

[MissMarple]

1. Is this like...math?

I don't do that. :D

[dsc]

2. I can try.

A unit circle is a circle whose radius is 1. That makes it's diameter 2, it's area pi, and it's circumference 2pi.

Pretend for the rest of this that this circle is centered at (0.0) on the coordinate axis. Then, four of it's points would be (1,0), (0,1), (-1,0), and (0,-1). Those would be 0,90,180, and 270 degrees respecively. To find the sin of the angle formed by any radius and the x axis one simply takes the y coordinate and divides 1 (the radius of the circle) that would be y. The x coordinate is the cosine. tan is y/x. sec is 1/sin, cot is 1/tan, and cosec is 1/cosine. Hope that helps.

[jiacinto]

4. Well

I could never see how then it can relate to periodic motion.

[dsc]

6. Imagine

the circle stretched out instead of as a circle. Ie imagine the top half of the circle where it is but the bottome half flipped with the hinge being (1,0). That is sort of how it works. It isn't exact but that gives a limited picture.

[kalashnikov]

3. SOA CAH TOA!

Sin=Opposit angle side/Adjacent
Cosine=Adjacent/Hypoteneus
Tangent=Opposite/Adjacent

thats all u need to know, Unit circle is stupid.

[MrSoundAndVision]

7. I remember too

that's all.

[neuvocat]

5. Oh boy!

That's almost a whole semester's worth of trig.

Imagine a circle with radius of "1". Now superimpose that circle on an X-Y coordinate plane with the center of the circle on the origin.

The X coordinate would measure a distance of "1", as would the Y coordinate. Remember that the coordinate plane is composed of four quadrants I, II, III, and IV.

If the tip of the radius is in quadrant I, then the coordinates would be two positive numbers (+,+). Quadrant II would have a negative X and positive Y, and so on. Remember that you are going in a counter-clockwise direction.

The X direction is like one side of a triangle and the Y direction is like another. The radius is like the hypotenuse. Sine, cosine, and tangent are ratios of each where the sine is the opposite over the hypotenuse, the cosine is the adjacent side over the hypotenuse and the tangent is the opposite side over the adjacent side. These sides are identified with an angle chosen between two of the sides.

SOHCAHTOA is the ratio you could use to remember how they are set up.

Anyways, that's all I can think of for now. Just keep in mind the Pythagorean theorem though, because it also comes into play if you have to solve for different sides.

[ChoralScholar]

8. The unit circle

makes it somewhat easier to deal with radians. And provides a simple way to remember the trig functions. Although, apparently it doesn't work, because I can't remember the trig functions as they relate to a unit circle. When I became a music major, I decided all I need to do is be able to count to four. :)