Question

Найдите значение sina, tga, и ctga если cos a равно =5/13​

Answer 1

Ответ:

$sin(a)=\sqrt{1-cos^{2}(a)} \\sin(a)=\sqrt{1-(\frac{5}{13} )^{2}}\\sin(a)=\sqrt{1-\frac{25}{169}}\\sin(a)=\sqrt{\frac{169}{169} -\frac{25}{169}}\\sin(a)=\sqrt{\frac{144}{169} }\\sin(a)=\frac{12}{13}$

$tg(a)=\frac{sin(a)}{cos(a)} \\tg(a)=\frac{\frac{5}{13} }{\frac{12}{13} } \\tg(a)=\frac{5}{13} *\frac{13}{12} \\tg(a)=\frac{5}{12}$

$ctg(a)=\frac{cos(a)}{sin(a)} \\tg(a)=\frac{\frac{12}{13} }{\frac{5}{13} } \\tg(a)=\frac{12}{13} *\frac{13}{5} \\tg(a)=\frac{12}{5} \\\\tg(a)=2,4$