find the exact value

Question

tan(x) = 7/24

 

180<x<270 

 

find cos (2x) 

 

please and and thank you 

Answer 1

Tan X = 7/24

 

 Tan^-1 ( 7/24) = 16.26/ Principal angle

 

    180 + 16.26 = 196.26

 

 Cos 2x = 1 - 2 Sin^2 X = 1 - 2 sin² ( tan^-1 ( 7/24) =

 

                                    = 1 - 2 . (7/ √( 7^2 + 24 ^2) )^2=

 

                                     = 1 - 2 . 49/ 625= 1 - 98/ 625= 0.8432

 

  Calculator:

 

   Cos ( 2 * tan^-1 ( 7/24)) = 0.8432     / Reading straight from the calculator.