вправа 14.8 гдз 10 клас математика Істер 2018

10 клас ➠ математика ➠ Істер
 
Вправа 14.8


Обчисліть:
1) 2sin π/12 cos π/12;
2) 2sin22°30'cos22°30';
3) sin 5π/12 cos 5π/12;
4) (sin75° + cos75°)2;
5) cos2 π/8 - sin2 π/8;
6) sin215° - cos215°.

 

Умова:


Відповідь - ГДЗ:

1) 2sin π/12 cos π/12 = sin2 • 75° =
= sin150° = sin(180° - 30°) = sin30° = 1/2;
2) 2sin22°30'cos22°30' = sin2 • (22°30') =
= sin45° = √2/2;
3) sin 5π/12 cos 5π/12 = 1/2 sin2 • 5π/12 =
= 1/2 sin 5π/6 = 1/2sin(π - π/6) =
= 1/2sin π/6 = 1/2 • 1/2 = 1/4;
4) (sin75° + cos75°)2 =
= sin275° + 2sin75°cos75° + cos275° =
= 1 + sin2 • 75° = 1 + sin150° =
= 1 + sin(180° - 30°) =
= 1 + sin30° = 1 + 1/2 = 1,5;
5) cos2 π/8 - sin2 π/8 =
= cos2 • π/8 = cos π/4 = √2/2;
6) sin215° - cos215° =
= -(cos215° - sin215°) =
= -cos2 • 15° = -cos30° = - √3/2.