Question

2cos^2x = 1

Solve for 0-360 degrees

Answer 1

45°, 135°, 225°, 315°

Explanation:

2cos²x = 1

cos²x = ½

cosx = +/- 1/sqrt(2)

Basic angle: 45

Since cos has both, positive and negative values, we'll consider all 4 quadrants

45,

180 - 45 = 135

180 + 45 = 225

360 - 45 = 315

Answer 2

45,135,315,225

Explanation:

2cos^2x = 1

Divide each side by 2

cos^2x = 1/2

Take the square root of each side

sqrt( cos^2 x) = ±sqrt (1/2)

cos x =±sqrt (1/2)

Make into two separate equations

cos x =sqrt (1/2) cos x = - sqrt(1/2)

Take the inverse cos of each side

cos ^-1 cos (x) = cos ^-1 (sqrt (1/2)) cos ^-1 cos (x) = cos ^-1 (-sqrt (1/2))

x = cos ^-1 (sqrt (1/2)) x = cos ^-1 (-sqrt (1/2))

x = 45 +360 n x = 135+ 360n

x = 315+360 n x =225+360n

Between 0 and 360

45,135,315,225