Plot the point (2,-7)




Draw a radius r from the origin to that point:



The angle the problem talks about is the one indicated by the 
counter-clockwise red arc.  The green arc is the reference angle:



Draw a line from (2,-7) perpendicular to the x-axis:



That makes a right triangle.  Label the horizontal side of the
triangle x=2 and the vertical side y=-7, the coordinates of the 
point (2,-7).



Now we calculate the radius r from the origin to the point (2,-7) by
the Pythagorean theorem:

r² = x²+y²
r² = (2)²+(-7)²
r² = 4+49
r² = 53
 r = √53

r is always taken as positive.



Now use the green angle and the sides of the right triangle:

sin(angle) =  =  =  =  

cos(angle) =  =  = 

tan(angle) =  =  =  = 

Edwin