1. Заполните таблицу, указав значения sin α, cos α, tg α и ctg α для углов по тригонометрической таблице: Варианты - номера 1, 5, 9, 13, 17, 21, 25 и 29 630° -510° 11π/4 -30π/4 Варианты - номера 3, 7, 11, 15, 19, 23, 27 и 31 810° -405° 19π/4 11π/4 Варианты - номера 2, 6, 10, 14, 18, 22, 26 и 30 420° -1080° 13π/3 7π/3 Варианты - номера 4, 8, 12, 16, 20, 24, 28 и 32 1230° -720° 32π/3 11π/2

Давайте заполним тригонометрическую таблицу для каждого варианта. Напомню, что синус и косинус имеют период 2π или 360°, тангенс и котангенс - π или 180°. Мы будем использовать эти свойства и приводить углы к значениям в диапазоне от 0 до 360° или от 0 до 2π, которые мы можем легко найти в таблице. **Варианты 1, 5, 9, 13, 17, 21, 25 и 29:** * **630°:** 630° - 360° = 270°. sin(270°) = -1; cos(270°) = 0; tg(270°) = не определен; ctg(270°) = 0 * **-510°:** -510° + 2*360° = 210°. sin(210°) = -1/2; cos(210°) = -√3/2; tg(210°) = √3/3; ctg(210°) = √3 * **11π/4:** 11π/4 - 2π = 3π/4. sin(3π/4) = √2/2; cos(3π/4) = -√2/2; tg(3π/4) = -1; ctg(3π/4) = -1 * **-30π/4**: -30π/4 + 8π = 2π/4 = π/2. sin(π/2) = 1; cos(π/2) = 0; tg(π/2) = не определен; ctg(π/2) = 0 **Варианты 3, 7, 11, 15, 19, 23, 27 и 31:** * **810°:** 810° - 2*360° = 90°. sin(90°) = 1; cos(90°) = 0; tg(90°) = не определен; ctg(90°) = 0 * **-405°:** -405° + 2*360° = 315°. sin(315°) = -√2/2; cos(315°) = √2/2; tg(315°) = -1; ctg(315°) = -1 * **19π/4:** 19π/4 - 4π = 3π/4. sin(3π/4) = √2/2; cos(3π/4) = -√2/2; tg(3π/4) = -1; ctg(3π/4) = -1 * **11π/4:** 11π/4 - 2π = 3π/4. sin(3π/4) = √2/2; cos(3π/4) = -√2/2; tg(3π/4) = -1; ctg(3π/4) = -1 **Варианты 2, 6, 10, 14, 18, 22, 26 и 30:** * **420°:** 420° - 360° = 60°. sin(60°) = √3/2; cos(60°) = 1/2; tg(60°) = √3; ctg(60°) = √3/3 * **-1080°:** -1080° + 3*360° = 0°. sin(0°) = 0; cos(0°) = 1; tg(0°) = 0; ctg(0°) = не определен. * **13π/3:** 13π/3 - 4π = π/3. sin(π/3) = √3/2; cos(π/3) = 1/2; tg(π/3) = √3; ctg(π/3) = √3/3 * **7π/3:** 7π/3 - 2π = π/3. sin(π/3) = √3/2; cos(π/3) = 1/2; tg(π/3) = √3; ctg(π/3) = √3/3 **Варианты 4, 8, 12, 16, 20, 24, 28 и 32:** * **1230°:** 1230° - 3*360° = 150°. sin(150°) = 1/2; cos(150°) = -√3/2; tg(150°) = -√3/3; ctg(150°) = -√3 * **-720°:** -720° + 2*360° = 0°. sin(0°) = 0; cos(0°) = 1; tg(0°) = 0; ctg(0°) = не определен * **32π/3:** 32π/3 - 10π = 2π/3. sin(2π/3) = √3/2; cos(2π/3) = -1/2; tg(2π/3) = -√3; ctg(2π/3) = -√3/3 * **11π/2:** 11π/2 - 4π = 3π/2. sin(3π/2) = -1; cos(3π/2) = 0; tg(3π/2) = не определен; ctg(3π/2) = 0 Таким образом, значения для тригонометрических функций будут: | Угол | sin α | cos α | tg α | ctg α | |-------------|-------------|-------------|--------------|--------------| | 630° | -1 | 0 | не определен | 0 | | -510° | -1/2 | -√3/2 | √3/3 | √3 | | 11π/4 | √2/2 | -√2/2 | -1 | -1 | | -30π/4 | 1 | 0 | не определен | 0 | | 810° | 1 | 0 | не определен | 0 | | -405° | -√2/2 | √2/2 | -1 | -1 | | 19π/4 | √2/2 | -√2/2 | -1 | -1 | | 11π/4 | √2/2 | -√2/2 | -1 | -1 | | 420° | √3/2 | 1/2 | √3 | √3/3 | | -1080° | 0 | 1 | 0 | не определен| | 13π/3 | √3/2 | 1/2 | √3 | √3/3 | | 7π/3 | √3/2 | 1/2 | √3 | √3/3 | | 1230° | 1/2 | -√3/2 | -√3/3 | -√3 | | -720° | 0 | 1 | 0 | не определен | | 32π/3 | √3/2 | -1/2 | -√3 | -√3/3 | | 11π/2 | -1 | 0 | не определен | 0 |