solve cos3x=1/3

Question

if in a triangle ABC angle a and angle b are the solution of the equation cos3x=1/3 then find the value of angle c?

Answer 1

cos(3x) = 1/3

 

Then, 3x = Cos^-1(1/3) or 360ˆ - Cos^-1(1/3)

 

         3x = 70.5° or 289.5°

 

So, x = 23.5° or 96.5°

 

∠c = 180° - 23.5° - 96.5° = 60°

 

Answer 2

cosine is positive in quadrants 1 and 4

 

3x = inverse-cosine(1/3) 

 

3x      = 70.52878....

 

 x= 23.509593122...

 

In quadrant 4, that is 336.49