Найти числовые значения всех остальных триногометрических функций по данному значению дной из них ,если 0 cos a=0.8 sin a=5/13 tg a=2.4 ctg a=7/24
1)Для сos(a)=0,8: sin^2(a) = 1 - cos^2(a) = 1 - 0,64 = 0,36 По условию 0 a лежит в первой четверти => sin, cos, tg и ctg - положительные sin(a)=0,6 tg(a)=sin(a)/cos(a)=0,6/0,8=3/4 ctg(a)=4/3 2) sin(a) = 5/13 cos^2(a) = 1 - sin^2(a) = 1 - 25/169 = 144/169 cos(a) = 12/13 tg(a) = (5/13)*(13/12) = 5/12 ctg(a) = 12/5 3) tg(a) = 2,4 tg^2(a) = 5,76 1 + tg^2(a) = 1/cos^2(a) => 1/cos^2(a) = 6,76 cos^2(a) = 1/6,76 = 100/676 cos(a) = 10/26 = 5/13 sin^2(a) = 1 - 25/169 = 144/169 sin(a) = 12/13 ctg(a) = (5/13)*(13/12) = 5/12 4) ctg(a) = 7/24 tg(a) = 24/7 ctg^2(a) = 49/576 1+ctg^2(a) = 1/sin^2(a) => 1/sin^2(a) = 1 + 49/576 = 625/576 sin^2(a) = 576/625 sin(a) = 24/25 cos^2(a) = 1 - sin^2(a) = 1 - 576/625 = 49/625 cos(a) = 7/25