5 Вычислите: a) sin 225 ° + cos 330° + ctg 510° 6) sin 17π + cos 14π - tg 13

а) sin 225° + cos 330° + ctg 510°

• sin 225° = sin (180° + 45°) = -sin 45° = -√2/2
• cos 330° = cos (360° - 30°) = cos 30° = √3/2
• ctg 510° = ctg (360° + 150°) = ctg 150° = ctg (180° - 30°) = -ctg 30° = -√3
• Сумма: -√2/2 + √3/2 - √3 = (-√2 + √3 - 2√3) / 2 = (-√2 - √3) / 2

б) sin(17π/6) + cos(14π/3) - tg(13π/4)

• sin(17π/6) = sin(2π + 5π/6) = sin(5π/6) = sin(150°) = 1/2
• cos(14π/3) = cos(4π + 2π/3) = cos(2π/3) = cos(120°) = -1/2
• tg(13π/4) = tg(3π + π/4) = tg(π/4) = 1
• Сумма: 1/2 - 1/2 - 1 = -1