solve the equation on the interval [0,2π]
\(\sqrt{2}cos(2\Theta)=1 \)
A. None of these
B. π/8, 7π/8, 9π/8, 15π/8
C. π/2, π, 3π/2, 2π
D. 5π/8, 7π/8, 13π/8, 15π/8
E. π/4, π/2, 3π/4, π
√2 cos(2 θ ) = 1 divide both sides by √2
cos (2 θ ) = 1 / √2
Let 2 θ = x
cos ( x) = 1 / √2 and this happens at x = pi/4 , 7pi/4 , 9pi/4 , 15pi/4
So
2 θ = pi/4, 7pi/4 , 9pi/4, 15pi/4 divide by 2
θ = pi / 8 , 7pi/ 8, 9pi / 8, 15pi / 8 answer "B"
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