Question

cos(x-π/6)=-.5
Find the exact solutions between
0 ≤ x ≤2π

Answer 1

\[
\cos( x -\frac \pi 6)= \cos(2 \frac \pi 3)
\]

Answer 2

\[

x -\frac \pi 6= \pm \frac {2 \pi} 3 + 2 k \pi

\]

Answer 3

\[
x = \frac \pi 6\pm \frac {2 \pi} 3 + 2 k \pi
\]
Choose the ones between 0 and 2 pi and you are done

Answer 4

i don't understand what you just did there

Answer 5

the last part i mean

Answer 6

i mean how do i pick one?

Answer 7

\[
\cos(u) = \cos(w) \implies x =\pm w + 2 k \pi

\]

Answer 8

You must get two solutions

Answer 9

\[
x = \frac \pi 6+ \frac {2 \pi} 3 + 2 0 \pi= \frac{ 5\pi} 6
\]
That is one

Answer 10

oh how did you know it was plus or minus 2π/3

Answer 11

It is not 20 pi it is 2 (0) pi=0 im the above post

Answer 12

\[
\cos \left(\pm\frac{2 \pi }{3}\right)=-\frac{1}{2}
\]

Answer 13

is it easier to graph it?

Answer 14

\[\cos \left( x-\frac{ \pi }{6 } \right)=-\frac{ 1 }{ 2 }=-\cos \frac{ \pi }{ 3 }=\cos \left( \pi-\frac{ \pi }{ 3 } \right) ,\cos \left( \pi+\frac{ \pi }{3 } \right)\]
\[\cos (x-\frac{ \pi }{6})=\cos \frac{ 2\pi }{3 },\cos \frac{ 4\pi }{3 }\]
\[x-\frac{ \pi }{ 6 }=\frac{ 4\pi }{6 }+2k \pi,\frac{ 8\pi }{6 }+2k \pi ,where~ k ~is~ an ~integer.\]
\[x=\frac{ 5\pi }{6 }+2k \pi,\frac{ \ 3\pi }{2 }+2k \pi ,where~ k~ is~ an~ integer\]~

Answer 15

could you draw out what you did there?

Answer 16

Here is the graph

Answer 17

how do i turn the decimals so it looks like pi/3 or something? i don't quite understand how to solve for x. am i suppose to add the .5 to the other side of the equation?

Answer 18

Please Read my older posts. I gave you some details

Answer 19

oh yeah i saw that, i didn't get how you got 2pi/3

Answer 20

I told you why
\[
\cos( 2 \pi/3)=-\frac 1 2=-.5
\]

Answer 21

and
\[
\cos( -2 \pi/3)=-\frac 1 2=-.5
\]