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December 3rd, 2016, 03:14 PM   #1
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Question Trying to understand sin and cos

I'm trying to understand sin and cos. What exactly are them.
I found this graph on the internet :

But it seems wrong. In a right triangle you can't find cathetus knowing just sin and cos of an angle. So what exactly is this graph trying to represent?
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December 3rd, 2016, 03:31 PM   #2
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you can if you know the hypotenuse (in this case the radius of the circle) is 1.
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December 3rd, 2016, 03:49 PM   #3
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Sin and Cos are both trigonometric functions. The graph you included is the unit circle. It is a circle with a radius of 1 that is placed at the origin of a Cartesian plane. The beauty of this is I can pick any point on that circle, and the x coordinate of that point with be my cos and the y coordinate will be my sin. I then draw a line from that point to the center of the circle (this will be my hypotenuse which will always equal 1). From my point, I also draw a vertical line to the x-axis. This vertical line is sin. From the base of that vertical line I can then draw a line back to the origin. This horizontal line is my cos.

We have now formed a triangle (like the one in your picture you showed us). Armed with the Pythagorean theorem, law of sines, law of cosines, etc, we can do a ton of cool things from here to solve triangles.

There are geniuses on here that will certainly laugh at my explanation, so take it with a grain of salt. Trigonometry is one of my favorite branches of mathematics so I figured I would leave my two cents.
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December 3rd, 2016, 04:53 PM   #4
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sin(theta) & cos(theta)

The sine of a degree, for example in your graph, sin(45, is the same as the saying to sine of 45 degrees is the opposite over hypotenuse. So sine of 45 degrees equals square root 2 over 2. sqrt(2)/2. Sine is also the y value of the point of your radius. On your graph it is also the length of the red line that has sine(theta) next to it.
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