Question

can someone help me solve cos(2x)= sqrt2/2?

Answer 1

cos(2x) = \[\sqrt{2}/2\]

Answer 2

do you have the unit circle with you?

Answer 3

yeah

Answer 4

which angle gives you an x coordinate of sqrt(2)/2

Answer 5

pi/4 and 7pi/4

Answer 6

so cos(pi/4) = sqrt(2)/2 and cos(7pi/4) = sqrt(2)/2

Answer 7

if you undo both sides with arccos, you get

pi/4 = arccos(sqrt(2)/2)

or

7pi/4 = arccos(sqrt(2)/2)

Answer 8

but its suppose to be cos (2x) = sqrt2/2

Answer 9

i know

Answer 10

so if you have

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

and you undo both sides with arccos, you get

2x = arccos(sqrt(2)/2))

Answer 11

which means

2x = pi/4

or

2x = 7pi/4

solve each for x to get

x = pi/8

or

x = 7pi/8


this is assuming x is some angle between 0 and 2pi radians

Answer 12

thanks that makes sense

Answer 13

yw