Explanation:
3. We know the x value which is -5 and the y value which is 1. We need to find the hypotenuse which we refer to the r. We use the pythagorean theorem for that
![{x}^(2) + {y}^(2) = {r}^(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/gz5fhgdz8x6agyemmiagl690h13xcgsd47.png)
![{ - 5}^(2) + {1}^(2) = r {}^(2)](https://img.qammunity.org/2022/formulas/mathematics/college/ggt7iw92kj55mbpgpbatgz0lqfoas4kidt.png)
![25 + 1 = r {}^(2)](https://img.qammunity.org/2022/formulas/mathematics/college/zkclb858x8wj1waik03tu9zu6lt9l4flue.png)
![26 = r {}^(2)](https://img.qammunity.org/2022/formulas/mathematics/college/5uoew4e7th9nb72v636c9mfhvgbzjckr5g.png)
![r = √(26)](https://img.qammunity.org/2022/formulas/mathematics/college/tblbti9cfx3h1v3iny9cmasmgitdzgcpmx.png)
Now let find the sin, csc, and tan.
To find sin let use the formula
![(y)/(r)](https://img.qammunity.org/2022/formulas/mathematics/college/icjrf7eoyc814g2jbprcpjgvgmcsre6jkp.png)
![(1)/( √(26) )](https://img.qammunity.org/2022/formulas/mathematics/college/xn22ssibznelarjo259zk3vshm0oqte9du.png)
Rationalize the denominator
![(1)/( √(26) ) * ( √(26) )/( √(26) ) = ( √(26) )/(26)](https://img.qammunity.org/2022/formulas/mathematics/college/1xxxep4q34mpjfi4dpswhaphl8zp7x87vr.png)
![\sin = ( √(26) )/(26)](https://img.qammunity.org/2022/formulas/mathematics/college/wighxr1lkrl0cwebt117vee4uiszvichoy.png)
To find cosecant, it is the reciprocal of sin so it would be
![\csc = (26)/( √(26) ) * ( √(26) )/( √(26) ) = √(26)](https://img.qammunity.org/2022/formulas/mathematics/college/nd0u56vnosq86h9x8aaz9weuqtsuoxub5q.png)
To find tan, do
![(y)/(x)](https://img.qammunity.org/2022/formulas/mathematics/high-school/kk47l7fcbc8hnd4gp58h6f1qp2hocyp8wd.png)
Which is simply
![\tan= (1)/( - 5)](https://img.qammunity.org/2022/formulas/mathematics/college/i41bs5sdns36fsyojoncwh4qj7uou1p2yw.png)
4. Kennedi is correct since in the 2nd quadrant
The x value is negative, and the y value is positive.
Since sin is referred in trig as the y value, sin must be positive.