How to solve sin [arccos(1/2)] without a calculator? Please help as soon as you can!

Question

anonymous · Answer

We could use our memory of the unit circle, but it would be a little tedious--and you couldn't do it for all types of problems. Let's draw a picture!

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Since the cosine of whatever this angle is 1/2, I know that I can assume it's fully reduced(in reality, it could be a triangle with a hypotenuse of 2000 and a bottom leg of 1000. It's the ratio that counts.)

What's the sine of theta? It's simply the leg opposite of theta divided by the hypotenuse. We already know the hypotenuse, so now let's find the other leg, or the height of the triangle.

Use the pythagorean theorem: sqrt(2^2-1^2)=sqrt(3)

So this means that the sine of whatever this angle is sqrt(3)/2--which means that it's pi/3, but you were only asked to find the sine.