Find an exact value. cos 165° quantity square root of six minus square root of two divided by four. quantity square root of two minus square root of six divided by four. quantity square root of two plus square root of six divided by four. quantity negative square root of six minus square root of two divided by four.

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Find an exact value. cos 165° quantity square root of six minus square root of two divided by four. quantity square root of two minus square root of six divided by four. quantity square root of two plus square root of six divided by four. quantity negative square root of six minus square root of two divided by four.

Mathematics
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\[\cos 165^{\circ} = -\cos (180^{\circ} - 165^{\circ})=-\cos(15^{\circ})\]\[= - \cos(45^{\circ} - 30^{\circ})\]
I thought you would do cos(165)=cos(120+45) for that part?
Anything that works...

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Okay can you help me do the problem that way?
\[\cos(120 + 45) = \cos 120 \cos 45 - \sin 120 \sin 45\]Do you know the values of the four trig-ratios?
Would I use the unit circle for that?
  • phi
yes, you can use the unit circle (at least to figure out the correct sign) for example, cos 120 on the unit circle we have |dw:1438101174265:dw|
  • phi
to find the cos 120, we first find the "principal angle" which is always the smallest angle measured from the x-axis. In this case it is the marked angle in the figure, and it is 180-120= 60 degrees thus we want to find the cos 60. This is one that should be memorized. cos 60= 1/2 Next, we need to figure out the sign. As shown in the figure, the "x value" is negative we know cos = x/r (r is 1 for the unit circle), so if x is negative, then the cosine value will be negative. All of that means cos 120 = - 1/2

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