Question

How do I evaluate sin(pi/3) without using a calculator?

Answer 1

you need to remember it or use a cheat sheet with a unit circle on it

Answer 2

it is a good idea to memorize it because it is always \(\frac{\sqrt3}{2}\) and you will see it again and again

Answer 3

and again and again and again and again

Answer 4

How is it \[\frac{ \sqrt{3} }{2 }\]
I know that sin = opp/hyp and that pi/3 = 60 degrees, but when I take the sin of 60 degrees (using the 30-60-90 triangle), I get 1/2.

Answer 5

refer to your unit circle diagram

Answer 6

by simple geometry \(\sin(\pi/3)=\cos(\pi/6)\)

Answer 7

\[so: 2^{2}= a ^{2}+1^{2}\rightarrow a=\sqrt{2^{2}-1^{2}}=\sqrt{3}\]

Then you know that :\[\frac{ \Pi }{ 2 } rad = 60º\]
so: \[\sin 60º= \frac{ \sqrt{3} }{ 2}\]