Construction of the angle 
produces a 30-60-90
triangle, which has angles 
and 
. From the above diagram, write 
for the vertical leg, then the horizontal leg is
given by
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(1)
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by the Pythagorean theorem. Now use the double-angle formula
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(2)
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to obtain
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(3)
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which can be solved for 
to yield
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(4)
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Filling in the rest of the trigonometric functions then gives
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(5)
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(6)
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(7)
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(8)
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(9)
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(10)
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