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January 6th, 2013, 12:45 PM   #1
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Trig Identities help, please

Hello, I'm working on a worksheet, and I'm stuck on this question, I think I missed the lesson on it, because I don't know how to solve any of it. Any help is much appreciated, here's the question:

Solve -2cosX - root3 = 0

a) How many solutions are possible?
b) In which quadrants would you find the solutions?
c) Determine the related angle for the equation.
d) Determine all the solutions for the equation.

For a, I think the answer is four, though I'm not sure, for b, I think the answer is all four quadrants, although again, I'm not sure. I still have no idea about question c or d.
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January 6th, 2013, 12:50 PM   #2
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Re: Trig Identities help, please

Solve the equation for cos(x)...what do you have?
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January 6th, 2013, 10:23 PM   #3
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Re: Trig Identities help, please

cos x = -root3 by 2
the sign minus indicates it is in 2nd and 3rd quadrant (ALL,SIN,TAN, ..1st,2nd,3rd,4th quadrant respectively have positive signs and we choose those in which cos is not positive)
and the basic acute angle for root 3 by 2 is 30(cos30=root3 by 2 you can easily get this from 30-60 rt triangle),
so the solutions are 150,210,360+150,360+210,720+150,720+210......
there are infinitely many solutions if the interval for x is not given (this is usually given).
I do not understand the meaning of related angle (maybe this refers to basic acute angle).
Sorry for my poor English,....
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