The Exact Value of sin(π/5) is Here in the Pentagon

Regular pentagons are amazing, aren't they!

[christianurso]

Its even more beautiful for the cosine of pi over five

[markusklyver]

sin(pi/5) has an exact value, it is exactly sin(pi/5)

[ankursadhukhan]

Sin and Cosine of 15°, 18°, 36°, 54°, 72° all has exact values.

[yuxplay]

What a beautiful demostration bro, still like this. Ever giving us good matematic vídeos.
Have an a beautiful day

[eve_the_eevee_rh]

How do we know the blue lines are, like, real, though? How do we know for certain they're all the same length

[lollol-ttfx]

fun fact:The sine of any angle has an exact value.

[rafaelcanha]

Its ((5-(5)^1/2/8)^1/2 idk why i cant get this result off my head

[SarojJha-oy]

Infact angle in degrees which is multiple of 3 has an exact value

[YassinePAN]

You can also use chebechve polynome n=5 and x=5 the gets the sin value it always works

[nbooth]

What exactly do people mean by "exact value"? Expressable as roots of a rational number?

[darksentinel]

I like how if something has to do with angles and the number 5, phi is always there

[Samir-zbxk]

I usually use Euler's formula for something like this. Cool to see a geometry way to do it

[JUGNUMEHROTRANEETASPIRANT]

Just use sin{π/10} = sin{18°} = {√(5)+1}/4, cos{x} = √[ 1 - sin^2{x} ] , & sin{2x} = 2.sin{x}.cos{x} .

[clementfradin]

You can also use De Moivre formula and solve an easy quintic equation

[Speakwastaken]

I was not expecting flowers and snail shells to show up here

[petevenuti]

It looks as if this could be used to create a matrix to transform π into ✓2.

[flexiumnova]

Wait how can you just "say" that those sides are all length a?

[The_Asteroid_]

Ohhh ! Thanks, I was not able to do that with the triangle.

[sergiocontrerask]

wow i never know if is possible splits 2 triangles

[reeb]

Does sin(pi/n) have an exact value for all rational numbers?