The terminal side of θ passes through the point (7,-1). what is the exact value of sinθ in simplified form?

Answer 

-1/√50

Explanation
We are going to take the angle ∅ to at the origin (at point (0, 0)).
The point (7, -1) means 7 units to the right and 1 unit downwards (negative side of y-axis).
This makes a  right triangle. The hypotenuse √(7²+1²) = √50

Now,
sine = opposite/hypotenuse
   
       = 1/√50

Angle ∅ is in the 4th quadrilant where the sine is egative.
so, the exact answer of sin∅ = -1/√50