Question

Plz help me find these functions!

Answer 1

Answer:

$\sin \alpha = \frac{5}{13}$, $\cos \alpha = \frac{12}{13}$, $\tan \alpha = \frac{5}{12}$, $\cot \alpha = \frac{12}{5}$, $\sec \alpha = \frac{13}{12}$, $\csc \alpha = \frac{13}{5}$

Step-by-step explanation:

The angle $\alpha$ 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:

$\sin \alpha = \frac{5}{\sqrt{5^{2}+12^{2}}}$

$\sin \alpha = \frac{5}{13}$

$\cos \alpha = \frac{12}{\sqrt{5^{2}+12^{2}}}$

$\cos \alpha = \frac{12}{13}$

$\tan \alpha = \frac{5}{12}$

$\cot \alpha = \frac{12}{5}$

$\sec \alpha = \frac{\sqrt{5^{2}+12^{2}}}{12}$

$\sec \alpha = \frac{13}{12}$

$\csc \alpha = \frac{\sqrt{5^{2}+12^{2}}}{5}$

$\csc \alpha = \frac{13}{5}$