# How do I solve this equation?

#### Karim

##### New member
I've been stuck on this equation for a while now and I need it to continue on with my question; how am I supposed to solve for:

f(x) = 2 in -2cos(3x)+1=2
I know that it'll eventually turn out to be; cos(3x) = -1/2 but what should I do after this?

#### Harry_the_cat

##### Elite Member
Do you mean "solve for x"?
Not sure what "solve for f(x)=2" means. Is f(x)=-2cos(3x)+1 ?

#### Karim

##### New member
Yes, I need to solve for x in the equation -2cos(3x)+1 = 2, without a calculator

#### Subhotosh Khan

##### Super Moderator
Staff member
Yes, I need to solve for x in the equation -2cos(3x)+1 = 2, without a calculator
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

Please share your work/thoughts about this problem.

#### Karim

##### New member

It's part b which I'm stuck on, I already found the values of a, k and c and made the equation, f(x) = -2 cos(3x) + 1

Uptil now, I've made it till here. I just don't know how to simplify it further.

#### Subhotosh Khan

##### Super Moderator
Staff member
View attachment 25418
It's part b which I'm stuck on, I already found the values of a, k and c and made the equation, f(x) = -2 cos(3x) + 1

View attachment 25419
Uptil now, I've made it till here. I just don't know how to simplify it further.
Now time to use unit circle!

Cos (t) = -1/2

t = ? ............................look at unit circle

2pi/3 and 4pi/3?

#### Harry_the_cat

##### Elite Member
Yes good. But there are more solutions when you consider angles coterminal with these.
So t = 2pi/3 +2k pi or 4pi/3 +2k pi where k is an integer.
But here t = 3x
So 3x = 2pi/3 + 2kpi or 4pi/3 + 2kpi
Divide both sides by 3
x = 2pi/9 +2kpi/3 or 4pi/9 + 2kpi/3
Now let k=0, 1, 2, etc until you pick up all the solutions between 0 and pi

Great thanks!