Sum of all real solutions

[philosopher]

This problem should be easy but for some reason I keep struggling with it.

When i sum all of the solutions i get 20/4π . But the answer is actually 19/4π.
I'm clearly doing something wrong here, it most likely has to do with the range of the functions.
Here's my work.
I would appreciate any help. Thanks.

 

[Dr.Peterson]

When i sum all of the solutions i get 20/4π . But the answer is actually 19/4π.
I'm clearly doing something wrong here, it most likely has to do with the range of the functions.

There are infinitely many real solutions! Surely there must be some restriction stated, such as all solutions in [MATH][0,2\pi)[/MATH]. Please state the entire problem exactly as given to you.

But if my guess is right, then you have included two solutions that are not in that interval; and you didn't do a necessary check on each solution to see if it satisfies the condition for its case.

 

[philosopher]

I somehow forgot to add that interval is (0,3π ). Sorry about that.

 

[pka]

This problem should be easy but for some reason I keep struggling with it.

When i sum all of the solutions i get 20/4π . But the answer is actually 19/4π.
I'm clearly doing something wrong here, it most likely has to do with the range of the functions.
Here's my work. I would appreciate any help. Thanks.

I agree with the given answer. Look here

 

[Dr.Peterson]

I somehow forgot to add that interval is (0,3π ). Sorry about that.

Then [MATH]19\pi/4[/MATH] is correct.

Do you see which one of your first three solutions is wrong, and what you need to use in place of your last two? You have the right ideas, but need to pay attention to the sign of the sine, as well as the interval.

 

[philosopher]

Then [MATH]19\pi/4[/MATH] is correct.

Do you see which one of your first three solutions is wrong, and what you need to use in place of your last two? You have the right ideas, but need to pay attention to the sign of the sine, as well as the interval.

Yep, got it now. Thanks a lot!

 

[Steven G]

You just can't say that |sin(x)| = sin (x) or |sin(x)| = -sin (x). This is NOT true.

Rather |sin(x)| = sin (x) if sin(x)>=0 OR |sin(x)| = -sin(x) if sin(x)<0