1. Cho ΔABC góc A bằng 90 độ AB=5cm , tan C= $\frac{5}{8}$ Tính AC , BC 2. Tính sina , cota , tana Biết cos a = $\frac{3}{5}$ 3. Tìn cosa , tan

Đáp án:

$\begin{array}{l}
1)tanC = \dfrac{{AB}}{{AC}} = \dfrac{5}{8} = \dfrac{5}{{AC}}\\
 \Rightarrow AC = 8\left( {cm} \right)\\
Do:A{B^2} + A{C^2} = B{C^2}\\
 \Rightarrow B{C^2} = {5^2} + {8^2} = 25 + 64 = 89\\
 \Rightarrow BC = \sqrt {89} \left( {cm} \right)\\
2)\\
\cos a = \dfrac{3}{5}\\
Do:{\cos ^2}a + {\sin ^2}a = 1\\
 \Rightarrow {\sin ^2}a = 1 – \dfrac{9}{{25}} = \dfrac{{16}}{{25}}\\
 \Rightarrow \left[ \begin{array}{l}
\sin a = \dfrac{4}{5}\\
\sin a = \dfrac{{ – 4}}{5}
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
{\mathop{\rm tana}\nolimits}  = \dfrac{{\sin a}}{{\cos a}} =  \pm \dfrac{4}{3}\\
\cot a =  \pm \dfrac{3}{4}
\end{array} \right.\\
3)\sin a = \dfrac{3}{5}\\
 \Rightarrow {\cos ^2}a = \dfrac{{16}}{{25}}\\
 \Rightarrow \cos a =  \pm \dfrac{4}{5}\\
 \Rightarrow \left\{ \begin{array}{l}
{\mathop{\rm tana}\nolimits}  = \dfrac{{\sin a}}{{\cos a}} =  \pm \dfrac{3}{4}\\
\cot a =  \pm \dfrac{4}{3}
\end{array} \right.
\end{array}$