Find the exact value of cos 480 degrees using the...

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tristatefabricatorsinc

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Jan 31, 2006
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Find the exact value of cos 480 degrees using the half-angle identity


I have so far...

sqrt(( 1 + cos960 degrees) / 2)

then making it
sqrt(( 1 + cos(1/2) / 2)

It does not seem to be coming out correctly for me when I solve it.

I keep getting sqrt(3/2)

I do not think this is correct though.
 
What does 960º have to do with anything?

Where is 480º? Is the cosine positive or negative, there?

Find a Reference Angle first.
 
You are making this a bit more difficult than it has to be. You can keep subtracting 360 from any angle bigger than 360 until it falls below 360.

For your problem, cos(480) = cos(480-360) = cos(120)

The reference angle in this problem will be 180-120 = 60 degrees. (If the idea of reference angles is not know to you, read your book a little)

The cosine of 60 (or Pi/3) is 1/2.
Since the angle in question is 120 (quadrant 2), you know that cosine is negative.

So, here is what we have done:
Cos(480) = cos(120) = -cos(60) = -1/2
 
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