Question

Дано: ctg a = - 7/24, если п/2 < a < п Найдите cos a, tg a, sin a.​

Answer 1

Ответ:

$ctga=-\frac{7}{24}\\\\\frac{\pi}{2}<a<\pi \; \; \Rightarrow \; \; sina>0\; ,\; \; cosa<0\; ,\; \; tga<0\\\\1+ctg^2a=\frac{1}{sin^2a}\; \; \to \; \; sin^2a=\frac{1}{1+ctg^2a}=\frac{1}{1+\frac{49}{576}} =\frac{576}{625}=(\frac{24}{25})^2\\\\sina=\frac{24}{25}>0\\\\sin^2a+cos^2a=1\; \; \to \; \; cos^2a=1-sin^2a=1-\frac{576}{625}=\frac{49}{625}=(\frac{7}{25})^2\\\\cosa=-\frac{7}{25}<0\\\\tga=\frac{1}{ctga}=-\frac{24}{7}$