If tanx=60/11 and π<x<3π/2 what is cos(x−π)?

Question

If  and  what is 

Enter your answer as a fraction in simplest form, like this: 3/14

Answer 1

Raquel, here's how to tackle this:

tan x = 60 / 11

Construct a right triangle with sides 11 and 60. The hypotenuse is √(11² + 60²) = √3721 = 61

Now, we can find all the other trig ratios for angle x: cos x = 11 / 61 and sin x = 60 / 61

Cos (x - π) = cos x cos π + sin x sin π

= (11/61) (-1) + 60/61 (0)

= -11/61