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?

Question

142673 views around the world

You can reuse this answer
Creative Commons License

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#