Answer:
[tex]\sin \alpha = \frac{5}{13}[/tex], [tex]\cos \alpha = \frac{12}{13}[/tex], [tex]\tan \alpha = \frac{5}{12}[/tex], [tex]\cot \alpha = \frac{12}{5}[/tex], [tex]\sec \alpha = \frac{13}{12}[/tex], [tex]\csc \alpha = \frac{13}{5}[/tex]
Step-by-step explanation:
The angle [tex]\alpha[/tex] is the angle opposite to the side of length 5 and adjacent to the side of length 12. From Trigonometry we remember the following relationships:
[tex]\sin \alpha = \frac{5}{\sqrt{5^{2}+12^{2}}}[/tex]
[tex]\sin \alpha = \frac{5}{13}[/tex]
[tex]\cos \alpha = \frac{12}{\sqrt{5^{2}+12^{2}}}[/tex]
[tex]\cos \alpha = \frac{12}{13}[/tex]
[tex]\tan \alpha = \frac{5}{12}[/tex]
[tex]\cot \alpha = \frac{12}{5}[/tex]
[tex]\sec \alpha = \frac{\sqrt{5^{2}+12^{2}}}{12}[/tex]
[tex]\sec \alpha = \frac{13}{12}[/tex]
[tex]\csc \alpha = \frac{\sqrt{5^{2}+12^{2}}}{5}[/tex]
[tex]\csc \alpha = \frac{13}{5}[/tex]
