No multiple choice, just an answer ?

Step-by-step explanation:

If the , then the cotangent is , given that:

, and .

This is important to know because if you recall the three Pythagorean identities in trigonometry, one of them involves a nice relationship between the cotangent and the cosecant of an angle:

so we can replace with 4/3, and find what is using that identity:

Now, you have to decide on which sign to use. So consider that if the tangent was positive, so most likely you are dealing with an angle between 0 and , and in that quadrant, the cosecant is positive.

Therefore, pick the positive value: 5/3