+37095 Since COT = +5 and COT = cos / sin we know that theta must be in 1st and 3rd quadrants
so cos/sin = 5 (this was given)
cos = 5 sin Now square both sides
cos^2 = 25 sin^2 (1st equation)
sin^2 + cos^2 = 1 so sin^2 = 1-cos^2 Sub this into 1st equation
cos^2 = 25(1-cos^2)
cos^2 = 25 - 25 cos^2 subtract cos^2 from both sides
0 = 25 - 26 cos^2 Subtract 25 from both sides
-25 = - 26 cos^2
25 = 26 cos^2
25/26 = cos^2
+- 5/ (sqrt 26 ) = cos theta
Sec theta = 1/cos = 1/ (+- 5/sqrt26) = sqrt 26 / 5 or - sqrt26 / 5
