đề sai nhỉ? sina/2; cos a/2; tana/2; cota/2 chứ?
ta có:
\(sin^2\dfrac{a}{2}=\dfrac{1-cosa}{2}=\dfrac{1-\dfrac{5}{13}}{2}=\dfrac{4}{13}\)
\(\dfrac{3\pi}{2}< a< 2\pi\Leftrightarrow\dfrac{3\pi}{4}< \dfrac{a}{2}< \pi\)
=> sina/2 > 0 => sina/2 = \(\dfrac{2}{\sqrt{13}}\)
ta có:
\(cos^2\left(\dfrac{a}{2}\right)=1-sin^2\left(\dfrac{a}{2}\right)=1-\dfrac{4}{13}=\dfrac{9}{13}\)
\(\dfrac{3\pi}{2}< a< 2\pi\Leftrightarrow\dfrac{3\pi}{4}< \dfrac{a}{2}< \pi\) (cung2)
=> cosa/2 < 0 => cosa/2 = \(\dfrac{-3}{\sqrt{13}}\)
\(tan\left(\dfrac{a}{2}\right)=\dfrac{sin\left(\dfrac{a}{2}\right)}{cos\left(\dfrac{a}{2}\right)}=\dfrac{\dfrac{2}{\sqrt{13}}}{-\dfrac{3}{\sqrt{13}}}=-\dfrac{2}{3}\)
\(cot\left(\dfrac{a}{2}\right)=\dfrac{1}{tan\left(\dfrac{a}{2}\right)}=\dfrac{1}{-\dfrac{2}{3}}=-\dfrac{3}{2}\)