4. sin(60°) = (√3)/2
cos(45°) = (√2)/2,
tg(30°) = 1/(√3)
(√6)*sin(60°)*cos(45°) + (√3)*tg(30°) = (√6)*( (√3)/2 )*( (√2)/2 )+(√3)*(1/√3) =
= ((√6)*(√6)/4 ) + 1 = (6/4) + 1 = (3/2)+1 = (3+2)/2 = 5/2 = 2,5.
5. sin(a) = 3/5.
cos²(a) + sin²(a) = 1,
cos²(a) = 1 - sin²(a),
cos(a) = √(1 - sin²(a)) = √(1 - (3/5)²) = √(25 - 9)/5 = √(16)/5 = 4/5
или cos(a) = -√(1-sin²(a)) = -4/5.
tg(a) = sin(a)/cos(a)
tg(a) = (3/5)/(4/5) = 3/4
или tg(a) = (3/5)/(-4/5) = -3/4.
ctg(a) = cos(a)/sin(a),
ctg(a) = (4/5)/(3/5) = 4/3
или ctg(a) = (-4/5)/(3/5) = -4/3.