Thread: A few Trig questions about radians/input/theory/etc. A beginner.

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!

Sine is the y value if r = 1

Originally Posted by Slappydappy

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!

360 degrees is 2pi radians.

It gives you the location in either radians or degrees. For instance, pi radians is 180 degrees.

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?

-140 can be re-written as 220 degrees

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.

-500+360+360=220

Angle -500 = -140 = 220 = 580 = .....





You can't take the since of -500 degrees in radians. You need to take it in degrees.

-500 radians isn't the same as -500 degrees.

I thought calculating -500 on a calculator (using the Radian function) calculated the Sine of that value at -500 Radians.

Originally Posted by Slappydappy

I thought calculating -500 on a calculator (using the Radian function) calculated the Sine of that value at -500 Radians.

It does but isn't the -500 degrees in your original post?

Oh I was just using the same number (for Degrees and Radians) to see the difference in the answers and ways of working them.