Для нахождения значений данных выражений, нам нужно использовать тригонометрические функции и их свойства. Давайте разберем каждое выражение по отдельности.

• sin135° = sin(180° - 45°) = sin45° = √2/2
• cos210° = cos(180° + 30°) = -cos30° = -√3/2
• tg405° = tg(360° + 45°) = tg45° = 1
• ctg330° = ctg(360° - 30°) = ctg30° = √3

Теперь подставим значения:

sin135° × cos210° × tg405° × ctg330° = (√2/2) × (-√3/2) × 1 × √3 = -3/4.

• sin225° = sin(180° + 45°) = -sin45° = -√2/2
• cos150° = cos(180° - 30°) = -cos30° = -√3/2
• ctg420° = ctg(360° + 60°) = ctg60° = 1/√3
• tg300° = tg(360° - 60°) = -tg60° = -√3.

Теперь подставим значения:

sin225° × cos150° × ctg420° × tg300° = (-√2/2) × (-√3/2) × (1/√3) × (-√3) = -√2/4.

• sin π/3 = √3/2
• cos 2π/3 = cos(π - π/3) = -cos π/3 = -1/2
• tg 7π/4 = tg(2π - π/4) = tg(-π/4) = -1
• ctg 13π/6 = ctg(2π + π/6) = ctg π/6 = √3.

Теперь подставим значения:

sin π/3 × cos 2π/3 × tg 7π/4 × ctg 13π/6 = (√3/2) × (-1/2) × (-1) × √3 = 3/4.

• sin 4π/3 = sin(π + π/3) = -sin π/3 = -√3/2
• cos 5π/6 = cos(π - π/6) = -cos π/6 = -√3/2
• tg 11π/4 = tg(2π + 3π/4) = tg 3π/4 = -1.
• ctg 19π/3 = ctg(6π + π/3) = ctg π/3 = 1/√3.

Теперь подставим значения:

sin 4π/3 × cos 5π/6 × tg 11π/4 × ctg 19π/3 = (-√3/2) × (-√3/2) × (-1) × (1/√3) = -3/4.

Таким образом, значения выражений:

• sin135° × cos210° × tg405° × ctg330° = -3/4
• sin225° × cos150° × ctg420° × tg300° = -√2/4
• sin π/3 × cos 2π/3 × tg 7π/4 × ctg 13π/6 = 3/4
• sin 4π/3 × cos 5π/6 × tg 11π/4 × ctg 19π/3 = -3/4