Question

Найди значениеcos(¥-60°),если sin¥=1/3 и 90°<¥<180° 1)2√2+√3/6 2)2-√3/6 3)-2√2+√3/6 4)2√2-√3/6 5)2√2-3/6

Answer 1

cos(ψ - 60°) = cos(ψ)*cos(60°) + sin(ψ)*sin(60°) = V,

sin(ψ) = 1/3,

cos(60°) = 1/2,

т.к. 90°<ψ<180°, то  cos(ψ) < 0, и

cos²(ψ) = 1 - sin²(ψ) = 1 - (1/3)² = 1 - (1/9) = 8/9,

cos(ψ) = -√(8/9) = -2*(√2)/3,

sin(60°) = (√3)/2,

V = ( -2*(√2)/3 )*(1/2) + (1/3)*(√3)/2 = -(√2)/3 + (√3)/6 = ( √3 - 2√2)/6.

Ответ. 3).