SOLUTION: Hi! If you could show you work for this that would be great. What is the exact value of sin pi/3 as found on the unit circle?

Question 1064795: Hi! If you could show you work for this that would be great.
What is the exact value of sin pi/3 as found on the unit circle?
Found 3 solutions by Alan3354, KMST, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Look up the unit circle.
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
As you know the circumference of a circle of radius R is .
For a , it would be .
So is the length of the unit circle circumference,
and the measure, in radians of the angle
that is a whole sweep around the unir circle.
Half of that, , is the measure of the angle that you know as ,
and in radians corresponds to
.
Think of triangle with three angles.
It is an equilateral triangle.
Here is such a triangle inside the unit circle:
Its altitude is ,
or (if we measure angles in radians)
.
The altitude divides the equilatetal triangle
into 2 right triangles.
The measure of the legs of those right trianglrs
are and .
The hypotenuse measures .
According to the Pythagorean theorem,

.
So, .
Answer by ikleyn(52878)   (Show Source): You can put this solution on YOUR website!
.
On unit circle see these links
https://en.wikipedia.org/wiki/Unit_circle
https://en.wikipedia.org/wiki/Unit_circle

and

https://en.wikipedia.org/wiki/Unit_circle#/media/File:Unit_circle_angles_color.svg
https://en.wikipedia.org/wiki/Unit_circle#/media/File:Unit_circle_angles_color.svg

You MUST KNOW and MEMORIZE / REMEMBER it as the multiplication table.

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