# Math Help - really easy trig question

1. ## really easy trig question

Hi,

I used to know this, now I can't remember.

Why is sin (pi/3) (rad) = (root 3)/2

Michael

2. Were you familiar with angles in degrees before? Like 60 degrees is pi/3 radians? Like 30 degrees is pi/6 radians?
If you were, then, maybe you still recall that:
"In a 30-60-90-degree right triangle, the leg opposite the 30 degrees is half in measure of the hypotenuse."

So the 30-60-90 right triangle has these:
hypotenuse = 2 units
leg opposite the 30-deg angle = 1 unit

the other leg, or the leg opposite the 60-deg angle is then sqrt(3) units.
why? because by Pythagorean theoem,
(one leg)^2 +(the other leg)^2 = (hypotenuse)^2
x^2 +1^2 = 2^2
x^2 +1 = 4
x^2 = 4 -1
x^2 = 3
x = sqrt(3)

Then, maybe you still know that:
sine = (opposite side)/(hypotenuse)

So if the angle is the 60 degrees,
sin(60deg) = (sqrt(3)) / 2

Then, since pi/3 rad = 60 deg, it follows that
sin(pi/3) = (sqrt(3)) / 2

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Why is pi/3 rad = 60 degree?

1 revolution = 360 deg
1 revolution = 2pi rad also
So,
1 rev = 1 rev
2pi rad = 360 deg
Divide both sides by 2,
pi rad = 180 deg
Divide both sides by 3,
pi/3 rad = 180/3 deg
pi/3 rad = 60 deg