Question

ПОМОГИТЕ! SIN.COS.TG

Answer 1

1) tg a = 2,4; a € (0; Π/2)
cos^2 a = 1/(1+tg^2 a) = 1/(1+5,76) = 1/6,76 = 100/676
cos a = 1/2,6 = 10/26 = 5/13
sin^2 a = 1 - cos^2 a = 1 - 100/676 = 576/676
sin a = 24/26 = 12/13
sin (60+a) = sin 60*sin a + cos 60*cos a = √3/2*12/13 + 1/2*5/13 = (5+12√3)/26

2) ctg a = 1 1/3 = 4/3; a € (0; Π/2)
tg a = 3/4
tg(45-a) = (tg 45 - tg a)/(1+tg 45*tg a) = (1-3/4)/(1+1*3/4) = (1/4)/(7/4) = 1/7

3) sin 150 = sin(180-30) = sin 30 = √3/2
cos 120 = cos(180-60) = -cos 60 = -1/2
tg 210 = tg(180+30) = tg 30 = √3/3
ctg 300 = ctg(360-60) = -ctg 60 = -√3/3
(√3/2*(-1/2)) / (√3/3*(-√3/3)) = (√3/4) / (1/3) = 3√3/4