Вычислите sina, cosa, tga и ctg заданного значения угла: a) 30; 6) 240; в)5π; г)7π

а) 30°

• sin(30°) = 1/2
• cos(30°) = √3/2
• tg(30°) = sin(30°) / cos(30°) = (1/2) / (√3/2) = 1/√3 = √3/3
• ctg(30°) = 1 / tg(30°) = √3

б) 240°

• 240° = 180° + 60°, следовательно, угол находится в третьей четверти, где синус и косинус отрицательны.
• sin(240°) = -sin(60°) = -√3/2
• cos(240°) = -cos(60°) = -1/2
• tg(240°) = sin(240°) / cos(240°) = (-√3/2) / (-1/2) = √3
• ctg(240°) = 1 / tg(240°) = 1/√3 = √3/3

в) 5π/6

• 5π/6 = 150°
• sin(5π/6) = sin(150°) = 1/2
• cos(5π/6) = cos(150°) = -√3/2
• tg(5π/6) = sin(5π/6) / cos(5π/6) = (1/2) / (-√3/2) = -1/√3 = -√3/3
• ctg(5π/6) = 1 / tg(5π/6) = -√3

г) 7π/4

• 7π/4 = 315°
• sin(7π/4) = sin(315°) = -√2/2
• cos(7π/4) = cos(315°) = √2/2
• tg(7π/4) = sin(7π/4) / cos(7π/4) = (-√2/2) / (√2/2) = -1
• ctg(7π/4) = 1 / tg(7π/4) = -1