a) Vì \(0 < α <  \frac{\pi}{2}\) nên \(\sinα > 0, \tanα > 0, \cotα > 0\)

• \(\sinα =  \sqrt{1-(\frac{4}{13})^{2}}=\frac{\sqrt{153}}{13}=\frac{3\sqrt{17}}{13}\)
• \(\cotα =  \left ( \frac{4}{13} \right )\div \frac{3\sqrt{17}}{13}=\frac{4\sqrt{17}}{51}\)
• \(\tanα =\frac{1}{cot\,\alpha}= \frac{3\sqrt{17}}{4}\)

b) Vì \(π < α <  \frac{3\pi }{2}\) 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) Vì \( \frac{\pi }{2} < α < π\) 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 \(\sinα < 0, \cosα > 0, \tanα < 0, \cotα < 0\)

• \(\tanα =  \frac{1}{\cot\alpha }=-\frac{1}{3}\)
• \(\sinα =  -\sqrt{\frac{1}{1+cot^{2}\alpha }}=-\sqrt{\frac{1}{10}}≈-0,3162\)
• \(\cosα =  \sqrt{\frac{1}{1+tan^{2}\alpha }}=\sqrt{\frac{1}{1+(\frac{1}{3}^{2})}}=\frac{3}{\sqrt{10}}≈0,9487\)