The point #(-4,10)# is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

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Answer 1 · 2016-12-14T18:33:35

Please see the explanation.

Let #x = -4#

Let #y = 10#

Let #r =# the length of a line segment drawn from the origin to the point:

#r = sqrt(x^2 + y^2)#

#r = sqrt((-4)^2 + 10^2)#

#r = sqrt(116) = 2sqrt(29)#

#sin(theta) = y/r#

#sin(theta) = 10/(2sqrt(29))#

#sin(theta) = (5sqrt(29))/29#

#csc(theta) = 1/sin(theta) = sqrt(29)/5#

#cos(theta) = x/r#

#cos(theta) = -4/(2sqrt(29))#

#cos(theta) = -(2sqrt(29))/29#

#sec(theta) = 1/cos(theta) = -sqrt(29)/2#

#tan(theta) = y/x#

#tan(theta) = 10/-4#

#tan(theta) = -2.5#

#cot(theta) = 1/tan(theta) = -2/5#