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find all 6 trigonometric functions of the angle whose terminal side goes through P(-4,6)

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This question simply tests your ability to recall the definitions of the trig functions.   To find all six functions you need to find x, y, and the hypotenuse of the ray going from the origin to P(-4, 6).   X=-4, Y = 6, and the hypotenuse can be found from r2 = x2 + y2
After finding r then use these definitions
sin = y/r
cos = x/r
tan = y/x
csc = r/y
sec = r/x
cot = x/y


If the terminal side goes through (-4,6)
R cannot be = 1
Find R as Isaac said with Pythagoras's Theorem.
If you want to find some easy ways to learn and remember the trig functions
look for Trig Without Tears on the internet.