Question

find all the solutions of 2 cos 3x=1 (0,2pi]
so i got cos 3x=1/2
or cos x=1/2
and i located it on the unit circle so i found pi/3, and 5pi/3
how do you find the other ones inbetween 0, 2pi please help

Answer 1

well
2cos(3x)=1
leads to
cos(3x) =1/2
as you said

Answer 2

now you know that 1/2 = cos(pi/3)

so you have: cos(3x) = cos(pi/3)

Answer 3

so you have:
3x = pi/3 + 360k
3x = -pi/3 + 360k

Answer 4

(for the general case: cos(x) = cos(a) the solutions are:
x = a + 360k
x = -a +360k
)

Answer 5

now using the equations you can get:
x = pi/9 + 120k
x=-pi/9 + 120k

plug in here different values of k such that the x's comes in the range

Answer 6

how did u get 120

Answer 7

i divided both sides of the equation by 3 (so i left with x in the left side)

Answer 8

look at my third response

Answer 9

it was better to write 2pi/3 instead of 120 since i used pi notation im sorry for that

Answer 10

ok i get that but they said the answers were( pi/9,5pi/9,7pi/9,`11pi/9,17pi/9) i got 5pi/9, pi/9 but how did they get the others

Answer 11

so we have:

x = pi/9 + (2pi/3)k
this gives:
k=0
pi/9
k=1
7pi/9
k=2
13pi/9
x=-pi/9 + (2pi/3)k
k=1
5pi/9
k=2
11pi/9
k=3
17pi/9

Answer 12

ok thanks