Sine is the y value if r = 1
Okay I've been trying my hardest to get the grasp of Trigonometry down, but I think I have overwhelmed myself. I have a few questions and I am going to try to word them so that they are not complicated and won't clutter up the thread.
1. What exactly is Sine (or Cosine)? The reason I ask, is because I was taught two things. One, that Sine is the Y-value on the Unit Circle or Graph. Secondly, that Sine is the ratio of Opposite/Hypotenuse in a Right Triangle. This confuses me because one seems to be a ratio and another a value (in Radians). I'm sure I've confused myself over nothing.
2. When I enter a value, such as X = -500 for Sine (y = Sine x), what does this value actually mean? Does it mean -500 degrees? Or -500 Radians? On a calculator, I plugged in -500 sine (in degrees) and it gives me -.64. -500 sine (in Radians) gives me .46. What do those values correspond to and why are the signs different? I assume they are the point on the Y-axis, but why are they different values and signs?
I guess I will stop there, since the answers to these may answer my other questions. Thanks to anyone that helps me!
Ok that helped me a little. So I am trying to work all this out by hand, so how does this work. If I have an angle that is -140 degrees, how do I manually figure out the Sine and Cosine on the unit circle? I drew a picture, but since I don't know the length of X or Y, I don't know how to proceed, all I have is the Angles and a radius of 1.
I drew a right triangle with a radius of 1 and angles 40 and 50 degrees inside. I'm not sure how to find Y or X for the triangle. I assume I HAVE to use a calculator or the calculation would take too long?
Ok I worked out two problems, one with Sine (-500) in Degrees and one with Sine (-500) in Radians. I am just doing this to help me understand all the concepts, I will end up using a calculator for everything once I get it.
1. Sine (-500) in Degrees gave me a Sine of -.64 and Cosine of -.766. So this is in Quadrant III. Also, the angle of measurement would be -500 degrees, -140 Degrees, or 220 degrees.
2. Sine (-500) in Radians gave me a Sine of .46 and Cosine of .883. So this is in Quadrant I. The angle of measurement would be -28, 647.27 degrees or 27.38 degrees.