Find all value of α in [0°, 360°) that will satisfy this equation? √2cos2α-1=0

1 Answer
Apr 8, 2018

x= 22.5°, 157.5°, 202.5°, 337.5°

Explanation:

sqrt2cos(2x)-1=0

Let 2x be u:
cos(u)= 1/sqrt2*sqrt2/sqrt2= sqrt2/2

u= pi/4+-2pin, (7pi)/4+-2pin

Now replace u with 2x and solve for x by dividing by 2:

2x= pi/4+-2pin, (7pi)/4+-2pin

x= pi/8+-pin, (7pi)/8+-pin where n ∈ Z

x= pi/8*(180°)/pi= 22.5°+180°(1)= 202.5°
x=(7pi)/8*(180°)/pi= 157.5°+180°(1)= 337.5°

x= 22.5°, 157.5°, 202.5°, 337.5°

graph{sqrt2cos(2x)-1 [-10, 10, -5, 5]}