a) Do \(0 < α < \frac{\pi}{2}\) nên \(\sinα > 0, \, \tanα > 0, \) \( \cotα > 0.\)
\(\sinα = \sqrt{1-(\frac{4}{13})^{2}}=\frac{\sqrt{153}}{13}=\frac{3\sqrt{17}}{13}\)
\(\cotα = \frac{4}{13}:\frac{3\sqrt{17}}{13}=\frac{4\sqrt{17}}{51}\); \(\tanα = \frac{3\sqrt{17}}{4}\)
b) \(π < α < \frac{3\pi }{2}\) nên \(\sinα < 0, \cosα < 0, \)\(\tanα > 0, \cotα > 0\)
\(\cosα = -\sqrt{(1 - sin^2 α)} = \)\(-\sqrt{(1 - 0,49) }= -\sqrt{0,51} ≈ -0,7141\)
\(\tanα ≈ 0,9802; \cotα ≈ 1,0202\).
c) \( \frac{\pi }{2} < α < π\) nên \(\sinα > 0, \cosα < 0,\)\( \tanα < 0, \cotα < 0 \)
\(\cosα = -\sqrt{\frac{1}{1+tan^{2}\alpha }}=-\sqrt{\frac{1}{1+(\frac{15}{7})^{2}}}\)\(=-\frac{7}{274}≈ -0,4229\).
\(\sinα = \sqrt{\frac{1}{1+cot^{2}\alpha }}=\sqrt{\frac{1}{1+(\frac{7}{15})^{2}}}=\frac{15}{\sqrt{274}}\)\(=0,9062\)
\(\cotα = - \frac{7}{15}\)
d) Vì \( \frac{3\pi}{2} < α < 2π\) nên \(\sinα < 0, \cosα > 0,\)\( \tanα < 0, \cotα < 0\)
Ta có: \(\tanα = \frac{1}{\cot\alpha }=-\frac{1}{3}\)
