A nick on the edge of a CD rotates to (−6, 5) during one song when represented graphically. What is the sine value of this function?

Question

valentina613 · Answer

The -6 and the 5 are the legs of a right triangle. 
 The hypotenuse can be found bt the pythagorean theorem: 
 H = sqrt((-6)^2 + 5^2) = 7.810 
 The value of the sine at that point would be: 
 sin(theta) = 5/7.81 = 0.6042

anonymous · Answer

Thanks! I got to the point at 7.810, but I do not understand why we are using the five to divide; can you please go more in depth with that part?
@valentina613

mathmale · Answer

Sketching this situation may help your understanding.
The point (-6,5) lies in the 2nd quadrant, in which the sine of the angle (measured from 0 degrees counterclockwise, into the 2nd quadrant) is 

$$\frac{ opp }{ hyp }=\frac{ 6 }{ \sqrt{[-6]^2+5^2} }=\frac{ 5 }{7.81  }$$

That "7.81" represents the length of the hypotenuse of the triangle formed by the point (-6,5).

anonymous · Answer

Can you draw a sketch of where the triangle would be? I can visualize the angle and terminal side, but not the triangle.

anonymous · Answer

@mathmale