Jawaban:

sin(2×π/5)

Exact result

sqrt(5/8 + sqrt(5)/8)

Decimal approximation

0.9510565162951535721164393333793821434056986341257502224473056444...

Conversion from radians to degrees

sin(72 °)

Reference triangle for angle (2 π)/5 radians

width | cos((2 π)/5) = 1/4 (sqrt(5) - 1)≈0.309017

height | sin((2 π)/5) = sqrt(5/8 + sqrt(5)/8)≈0.951057

Alternate forms

1/2 sqrt(1/2 (5 + sqrt(5)))

1/4 5^(1/4) (sqrt(1 - 2 i) + sqrt(1 + 2 i))

Minimal polynomial

16 x^4 - 20 x^2 + 5

Number line

Number line

Continued fraction

[0; 1, 19, 2, 3, 6, 5, 1, 1, 1, 3, 2, 1, 25, 2, 2, 1, 1, 11, 1, 2, 1, 7, 1, 1, 10, 1, 7, 23, ...]

Alternative representations

sin((2 π)/5) = 1/csc((2 π)/5)

sin((2 π)/5) = cos(π/2 - (2 π)/5)

sin((2 π)/5) = -cos(π/2 + (2 π)/5)

Series representations

sin((2 π)/5) = 2 sum_(k=0)^∞ (-1)^k J_(1 + 2 k)((2 π)/5)

sin((2 π)/5) = sum_(k=0)^∞ ((-1/100)^k (-π)^(2 k))/((2 k)!)

sin((2 π)/5)∝( sum_(k=0)^∞ (-1)^k d^(2 k)/(d((2 π)/5)^(2 k)) δ((2 π)/5))/θ((2 π)/5)

Integral representations

sin((2 π)/5) = (2 π)/5 integral_0^1 cos((2 π t)/5) dt

sin((2 π)/5) = sqrt(π)/(10 i) integral_(-i ∞ + γ)^(i ∞ + γ) e^(-π^2/(25 s) + s)/s^(3/2) ds for γ>0

sin((2 π)/5) = sqrt(π)/(2 i π) integral_(-i ∞ + γ)^(i ∞ + γ) (5^(-1 + 2 s) π^(1 - 2 s) Γ(s))/Γ(3/2 - s) ds for 0<γ<1

Multiple-argument formulas

sin((2 π)/5) = 3 sin((2 π)/15) - 4 sin^3((2 π)/15)

sin((2 π)/5) = 2 cos(π/5) sin(π/5)

sin((2 π)/5) = U_(-3/5)(cos(π)) sin(π)

by:Ken saka✓