Найти sin, cos, tg cos a =5/13, если 3Π/2 <=a<=2Π

Question

Найти sin, cos, tg
cos a =5/13, если 3Π/2 <=a<=2Π

Answer 1

Sin2a=2sina cosa
sina = -5/13
Найдем cosa
sin²a+cos²a=1 , откуда cos²=1-sin²a=1-(-5/13)²=1 - 25/169= (169-25)/169=144/169
πcosa=-√(144/169)= -12/13

sin2a=2sina cosa=2 (-5/13)(-12/13)=2*5*12/13² =120/169