# Unit Circle

[SOLVED] Unit Circle

How can I use the unit circle to get the right answer. I understand the 30 60 90 and 45 45 90 triangles, but come to a problem when using this method with cosine. For example cosine(3pi/2) is -[2^(1/2)]/2. Using my method I get the positive. Please explain the methods of using the unit circle.

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Have you learned about reference angles?

Let's use this Unit Circle as our guide: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf go to page 3.

Ok let's start in Quadrant 1. We know the Trigonometric values for 30-60-90 are for Cosine & Sine are ... refer to page 3.

Well if we look at Quadrant 2, and use our knowledge about reference angles, we can see that the trigonometric values for 30 & 150 are the same, except that cosine is negative.

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Not sure what exactly are reference angles, but I do know how to convert from radians to degrees.

Yes they are the same, but negative why exactly?

Yes they are the same, but negative why exactly?
Are you in the positive or negative x direction? If you go around the unit circle, in quadrant 2, only the x-values became negative.

In quadrant 3, both x and y are negative, but in quadrant 4, only the y-values are negative.

Quadrant 1: positive x and y
Quadrant 2: negative x and positive y

etc

30 degrees and 150 degrees are reference angles bc 180 - 150 = 30. Same goes for 135, 180 - 135 = 45.

If you start on the negative x-axis, and draw an angle towards the positive y-axis in a clock-wise direction, isn't that basically the same as drawing a 30 degree angle in the positive x-axis going in a counter-clockwise direction except in a different quadrant?

Both of these have hypotenuse 1, originating from the Origin. So now draw a 150 degree angle coming from the positive x-axis, you're triangle isn't going to have a 150 degree angle, that's not how we draw it. It's actually the remaining 30 degrees left that will form the angle for your triangle.

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Okay so if I was to use cosine which is X/R. I would receive a negative answer because of the negative x. Tell me if I'm wrong.

Okay so if I was to use cosine which is X/R. I would receive a negative answer because of the negative x. Tell me if I'm wrong.

Thx for the help rocomath I think I can handle it myself from here.

HallsofIvy