SOLUTION: How do I prove cos(pi/6)=sqrt(3)/2 knowing that sin(pi/6)=1/2?

Question 786238: How do I prove cos(pi/6)=sqrt(3)/2 knowing that sin(pi/6)=1/2?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If you were taught that
you would use that and the fact that is in the first quadrant, where sine and cosine are positive.

Otherwise, if you were only taught that sine and cosine are trigonmetric ratios that apply to right triangles, use a right triangle with a angle and hypotenuse length 1. Then invoke the Pythagorean theorem. The measures of the legs of that right triangle are and .

In fact, if you split an equilateral triangle in half using a median (connecting the midpoint of one side to the opposite vertex), you would get two congruent right triangles with one angle. Fron that idea, you can deduce both values, and . The shorter leg of those traingles, opposite the angle is half of the side of the equilateral triangle, that is now the right triangle's hypotenuse. Hence
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