Solve the equation on the interval 0 ≤ θ

Question

Solve the equation on the interval 0 ≤ θ < 2π.

Solve the equation on the interval 0 ≤ θ < 2π.

2 cos2 θ - 1 = 0

it says that the answer its

anonymous · Answer

pi/4 3pi/4 5pi/4 and 7pi/4 Why?

anonymous · Answer

well, those aren't the answers..

anonymous · Answer

Can you explain the answers?

anonymous · Answer

2 cos2x -1 = 0
2 cos2x = 1
cos2x =1/2
=> 2x = 60degrees or 150degrees
=> x = 30degrees or 75degrees...

anonymous · Answer

which one is the correct problem:

$\large 2cos^2\theta-1=0 $      OR    $\large 2cos(2\theta)-1=0 $

????

anonymous · Answer

@dpaInc that's the matter..the first one is the equation..because it gives an answer from the answer choices

anonymous · Answer

This $$2\cos ^{2}\theta-1=0$$

anonymous · Answer

ok then.... to solve for theta,
add 1 to both sides,
divide by 2 to both sides,
square root both sides....

then use the unit circle to determine what angles give you the necessary condition on the right side of the equation.