Question

Which of the following is a solution to cos(2x) = 1/2

60°
120°
150°
330°

Answer 1

@e.mccormick

Answer 2

@iGreen

Answer 3

@saifoo.khan

Answer 4

@jdoe0001

Answer 5

@iGreen

Answer 6

\(\bf cos(2x)=\cfrac{1}{2}\implies cos^{-1}[cos(2x)]=cos^{-1}\left( \cfrac{1}{2} \right)\implies 2x=cos^{-1}\left( \cfrac{1}{2} \right)
\\ \quad \\
x=\cfrac{cos^{-1}\left( \frac{1}{2} \right)}{2}\)

Answer 7

I cant find the degrees

Answer 8

well... what's the angle that \(\bf cos^{-1}\left( \cfrac{1}{2} \right)\)?

Answer 9

is positive, and cosine is only positive in the 1st and 4th quadrants

Answer 10

150 degrees

Answer 11

150 is on the 2nd quadrant

Answer 12

so its either a or d

Answer 13

in case you don't have a Unit Circle -> http://www.sciencedigest.org/UnitCircle.gif

Answer 14

how is 150 the second quadrant?

Answer 15

maybe im looking at it wrong

Answer 16

150 = 90 + 60

Answer 17

so 60 is in the 1st quadrant?

Answer 18

60 degrees

Answer 19

yeap.. notice your Unit Circle

Answer 20

so the answer is in the 4th quadrant?

Answer 21

either of those have a cosine of 1/2
thus let's say, using \(\pm 60\) in this case \(\bf cos(2x)=\cfrac{1}{2}\implies cos^{-1}[cos(2x)]=cos^{-1}\left( \cfrac{1}{2} \right)\implies 2x=cos^{-1}\left( \cfrac{1}{2} \right)
\\ \quad \\
x=\cfrac{cos^{-1}\left( \frac{1}{2} \right)}{2}\implies x=\cfrac{\cancel{\pm60}}{\cancel{2}}\to \pm30^o\)

Answer 22

So it is 60 degrees thanks