/sci/ - Science & Math

[Anonymous No.1971757]

What is the exact value of sin(3)? Is it possible to derive it from the identity sin(18 - 15)?

[Anonymous No.1971777]

Are you using degrees or radians? Hopefully degrees.

[Anonymous No.1971781]

.0523359562

[Anonymous No.1971784]

>>1971777
Yes, degrees.
I also know the exact value of sin(15), but not sin(18).

And by exact values, I obviously mean no decimals.

[Anonymous No.1973124]

Hmm, you can use;
sin(15) = sin(5*3)

http://www.wolframalpha.com/input/?i=sin%285a%29

So lets call x = sin(3), then you get
sin(15) = x⁵+5x(1-x²)²-10x³(1-x²) = 16x⁵-20x³+5x

Solve this and you obtain
http://www.wolframalpha.com/input/?i=x^5%2B5x%281-x^2%29^2-10x^3%281-x^2%29+%3D+Sin[15]
(the second to last was the true solution. way to big to copy over here)

[Anonymous No.1973139]

Actually, it could be simplified to "only"

1/2 sqrt((9-sqrt(5)-sqrt(6 (5+sqrt(5))))/(2(4+sqrt(7+sqrt(5)+sqrt(6 (5+sqrt(5)))))))

[Anonymous No.1973164]

Exact value of sin(3) is sin(3). Just like the exact value of 1/2 is 1/2, NOT 0.5. Why do you need it anyways?