Question

solve for x cos2x=(root3)/2

Answer 1

x = 15 or 345

Answer 2

how?

Answer 3

We can think of it this way:

Cos of (some angle) = sqrt(3) / 2

Well, what angles make cos = sqrt(3)/2 ?

Now just take those angles, and divide it by 2, since it's really

cos (two times some angle...) = sqrt(3)/2

Do you know how to draw a reference triangle?

Answer 4

so its pi/3
and then divide it by 2?

Answer 5

\[\cos \theta = \frac{\sqrt{3}}{2}\]for\[\theta = 30^o + 2k(360^o)\]or\[\theta = 330^o+2k(360^o)\]where k is an integer. Take k=0 for principal branch. Then for\[\theta =2x\]\[x=15^o , 165^o\]

Answer 6

\[\frac{\pi}{12}, \frac{11\pi}{12}\]

Answer 7

lokisan where have you been?

Answer 8

You can obtain these values for the argument of a trig. function from the unit circle.

Answer 9

lokisan not 165

Answer 10

http://en.wikipedia.org/wiki/File:Unit_circle_angles_color.svg

With color!!

Print it, frame it. :D

Answer 11

\[\cos (2 \times 165^o)=\cos(330^o)=\cos(360^o-30^o)=\cos(30^o)=\frac{\sqrt{3}}{2}\]

Answer 12

Hi myininaya, I've been studying/lecturing :)

Answer 13

cool!