Find all solutions in ​[0 degrees​, 360 degrees​). 2cos(x)-1=0.4136

Answer 1

2cosx-1=0.4136

2cosx=1.4136

cosx=0.7068

x=cos^-1(0.7068)=45.02 degrees or 0.786 radians

Since cosine is positive in quadrant I (positive x, positive y) and IV (positive x, negative y), the answers will be ±45.02 degrees or ±0.786 radians.

Shortcut: 1.4136 is approximately the square root of 2 (1.414). If you didn't have a calculator or were rushed for time on an exam, you could approximate cosx as √2/2, giving x=±45 degrees or π/4=0.785 radians.