What is the value of sin 0 given that (5, -12) is a point on the terminal side of 0 ?

The first choice is the one you want.

Step-by-step explanation:

If we plot the point (5, -12) we will be in QIV.  Connecting the point to the origin and then drawing in an altitude to the positive x axis creates a right triangle with side adjacent to the angle being 5 units long, and the altitude being |-12|.  To find the sin of theta, we need the side opposite (got it) over the hypotenuse (don't have it).  We solve for the length of the hypotenuse using Pythagorean's Theorem:

and

so

c = 13.  

Now we can find the sin of the angle in the side opposite the angle over the hypotenuse:

The first choice in your answers is the one you want.

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