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# Trig Equation Watch

1. I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
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2. (Original post by samjohnny)
I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
Okay, so let's say I had and I had to solve it in the range (degrees), I would solve it normally, by using the sine graph or the CAST diagram.

However, if I had and I had to solve it in the range (degrees), because I no longer am dealing with x - instead I'm dealing with x+20 - my range must change. It will now become:

Hence, I have to extend my sine graph (or continue to use the CAST diagram) to find other solutions in that range. Do you get what I'm trying to say? So, what would your range become?

You also might want to check the two answers you have - I don't quite understand what you've done.
3. (Original post by samjohnny)
I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
so we must consider giving 5 solutions
4. Ah right, I get it now. Thanks a lot.

I'm also having a hard time on the one after it. It's attached. Not sure where to start or how to follow through.
Attached Images

5. (Original post by samjohnny)
Ah right, I get it now. Thanks a lot.

I'm also having a hard time on the one after it. It's attached. Not sure where to start or how to follow through.
You want to use the hint they've provided to combine a couple of the cosine terms. Have a play with it and see if you can work out which two can be usefully combined.
6. (Original post by samjohnny)
I've solved the attached equation and got 5pi/20 and 13pi/20, but was informed there are three more solutions. From obtaining 5x - pi/4= pi + n2pi where n is an integer I just followed on algebraically until I got my two solutions. How do I obtain the missing ones?
Firstly
You should to consider that the sine function is periodic and to solve
the equation according to this generally

e.g. 1. When

then

or

That is
First solution sequence

and the second solution sequence

Secondly.
From general solutions you have to choose those whiches are in the
given range for

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