An angle Ɵ in standard position for which terminal side passes through the point (-1, 2), how do you find the six trig functions for Ɵ?

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Answer 1 · 2016-10-22T19:32:50

Please see the explanation for the "How to".

Cartesian points can be specified using a radius, #r#, and an angle, #theta#, as follows:

#x = (r)cos(theta) and y = (r)sin(theta))#

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

For the point #(-1, 2)#:

#r = sqrt((-1)^2 + 2^2)#

#r = sqrt(5)#

Substitute this information into the equations for x and y:

#-1 = (sqrt(5))cos(theta) and 2 = (sqrt(5))sin(theta))#

#cos(theta) = -1/sqrt(5) and sin(theta) = 2/sqrt(5)#

Move the radicals to the numerators:

#cos(theta) = -sqrt(5)/5 and sin(theta) = 2sqrt(5)/5#

#sec(theta) = 1/cos(theta)#

#sec(theta) = -sqrt(5)#

#csc(theta) = 1/sin(theta)#

#csc(theta) = sqrt(5)/2#

#tan(theta) = y/x#

#tan(theta) = 2/-1#

#tan(theta) = -2#

#cot(theta) = 1/tan(theta)#

#cot(theta) = -1/2#