Question

ВыразитеА)cos a,tg a и ctg a через sin aб)sin a,tg a и ctg a через cos ав)sin a,cos а и ctg a через tg aг)sin a,cos а и tg a через ctg a

Answer 1

А) cos $\alpha$=$\sqrt{ 1^{2}- sin^{2} \alpha }$
    tg $\alpha$=$\frac{sin \alpha }{cos \alpha }$
    ctg $\alpha$=$\frac{cos \alpha }{sin \alpha }$
б) sin $\alpha$=$\sqrt{1^{2}-cos^{2} \alpha }$
    tg $\alpha$=$\frac{sin \alpha }{cos \alpha }$
    ctg $\alpha$=$\frac{cos \alpha }{sin \alpha }$
в) sin $\alpha$=$tg \alpha *sin \alpha$
    cos $\alpha$=$\frac{sin \alpha }{tg \alpha }$
    ctg $\alpha$=$\frac{1}{ctg \alpha }$
г) sin $\alpha$=$\frac{cos \alpha }{ctg \alpha }$
    cos $\alpha$=$sin \alpha * ctg \alpha$
    tg $\alpha$=$\frac{1}{ctg \alpha }$

Answer 2

Ответы через sin(a):

а) cos(a) = √(1 - sin^2(a)) tg(a) = sin(a) / √(1 - sin^2(a)) ctg(a) = √(1 - sin^2(a)) / sin(a)

б) sin(a) = tg(a) / √(1 + tg^2(a)) tg(a) = sin(a) / √(1 - sin^2(a)) ctg(a) = √(1 - sin^2(a)) / sin(a)

в) sin(a) = √(1 - cos^2(a)) cos(a) = √(1 - sin^2(a)) ctg(a) = cos(a) / sin(a)

г) sin(a) = √(1 - tg^2(a)) cos(a) = 1 / √(1 + tg^2(a)) tg(a) = sin(a) / cos(a)

Ответы через cos(a):

а) cos(a) = √(1 - sin^2(a)) tg(a) = sin(a) / √(1 - sin^2(a)) ctg(a) = √(1 - sin^2(a)) / sin(a)

б) sin(a) = √(1 - cos^2(a)) tg(a) = sin(a) / cos(a) ctg(a) = cos(a) / sin(a)

в) sin(a) = √(1 - cos^2(a)) cos(a) = √(1 - sin^2(a)) ctg(a) = cos(a) / sin(a)

г) sin(a) = √(1 - cos^2(a)) cos(a) = 1 / √(1 + tg^2(a)) tg(a) = sin(a) / cos(a)

Ответы через tg(a):

а) cos(a) = 1 / √(1 + tg^2(a)) sin(a) = tg(a) / √(1 + tg^2(a)) ctg(a) = 1 / tg(a)

б) sin(a) = tg(a) / √(1 + tg^2(a)) cos(a) = 1 / √(1 + tg^2(a)) ctg(a) = 1 / tg(a)

в) sin(a) = tg(a) / √(1 + tg^2(a)) cos(a) = 1 / √(1 + tg^2(a)) ctg(a) = 1 / tg(a)

г) sin(a) = tg(a) / √(1 + tg^2(a)) cos(a) = 1 / √(1 + tg^2(a)) tg(a) = sin(a) / cos(a)

Ответы через ctg(a):

а) cos(a) = √(1 - ctg^2(a)) sin(a) = √(1 - ctg^2(a)) / ctg(a) tg(a) = 1 / ctg(a)

б) sin(a) = ctg(a) / √(1 + ctg^2(a)) cos(a) = 1 / √(1 + ctg^2(a)) tg(a) = 1 / ctg(a)

в) sin(a) = ctg(a) / √(1 + ctg^2(a)) cos(a) = 1 / √(1 + ctg^2(a)) tg(a) = 1 / ctg(a)

г) sin(a) = ctg(a) / √(1 + ctg^2(a)) cos(a) = 1 / √(1 + ctg^2(a)) tg(a) = 1 / ctg(a)