Question

Plz help me find these functions!

Answer 1

`\sin \alpha = (5)/(13)`,
`\cos \alpha = (12)/(13)`,
`\tan \alpha = (5)/(12)`,
`\cot \alpha = (12)/(5)`,
`\sec \alpha = (13)/(12)`,
`\csc \alpha = (13)/(5)`

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 = (5)/(13)`

`\cos \alpha = \frac{12}{\sqrt{5^(2)+12^(2)}}`

`\cos \alpha = (12)/(13)`

`\tan \alpha = (5)/(12)`

`\cot \alpha = (12)/(5)`

`\sec \alpha = \frac{\sqrt{5^(2)+12^(2)}}{12}`

`\sec \alpha = (13)/(12)`

`\csc \alpha = \frac{\sqrt{5^(2)+12^(2)}}{5}`

`\csc \alpha = (13)/(5)`