sin(60°) = √3/2
Так как cos(π/2 + a) = 1/2, то sin(π/2 + a) = ±√(1 - cos^2(π/2 + a)) = ± √(1 - 1/4) = ± √(3/4) = ± √3/2
Так как π < a < 3π/2, то синус отрицателен, значит sin(π/2 + a) = -√3/2
Теперь найдем sin(60° + a):sin(60° + a) = sin(π/3 + a) = sin(π/3)cos(a) + cos(π/3)sin(a) = (√3/2)cos(a) + (1/2)sin(a) = (√3/2)(√3/2) + (1/2)(-√3/2) = 3/4 - √3/4 = (3 - √3)/4.
sin(60°) = √3/2
Так как cos(π/2 + a) = 1/2, то sin(π/2 + a) = ±√(1 - cos^2(π/2 + a)) = ± √(1 - 1/4) = ± √(3/4) = ± √3/2
Так как π < a < 3π/2, то синус отрицателен, значит sin(π/2 + a) = -√3/2
Теперь найдем sin(60° + a):
sin(60° + a) = sin(π/3 + a) = sin(π/3)cos(a) + cos(π/3)sin(a) = (√3/2)cos(a) + (1/2)sin(a) = (√3/2)(√3/2) + (1/2)(-√3/2) = 3/4 - √3/4 = (3 - √3)/4.