Find the values of the 6 trig functions if cos(2x) = 1/sqrt2 and is in QIII

Question

Find the values of the 6 trig functions if cos(2x) = 1/sqrt2 and is in QIII

Answer 1

1/sqrt(2) = sqrt(2)/2 

arccos[sqrt(2)/2] = 45° 

cos(360° + 45°) = cos(405°) = cos(45°)

If 2x = 405, then x = 202.5 which is in the 3rd quadrant

 

I will let you look up the trig functions of that angle.