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

Question

sinP=

cosP=

tanP=

 

cscP=

secP=

cotP=

Answer 1

(-4,6) is in the 2nd quadrant. where sines & cosecants are > 0 but the other 4 trig functions are negative

sinA = opposite side/hypotenuse = 6/(sqr(36+16) = 6/sqr52 = 3/sqr13

cscA = 1/sinA = sqr13/3

cosA = -4/sqr52 = -2/sqr13

secA = -sqr13/2

tanA = 6/-4 = -3/2

cotA =1/tanA = -2/3

Answer 2

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