How do I solve this equation?

Karim

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Apr 11, 2019
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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

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

Karim

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

Subhotosh Khan

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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

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1614531403803.png
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

1614531521654.png
Uptil now, I've made it till here. I just don't know how to simplify it further.
 

Subhotosh Khan

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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
 

Karim

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2pi/3 and 4pi/3?
 

Harry_the_cat

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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
 

Karim

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Great thanks!
 
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