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March 4th, 2011, 08:50 PM   #1
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Trigonometry

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March 4th, 2011, 09:51 PM   #2
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Re: Trigonometry

1)

Apply the double-angle identities for sine and cosine:



Divide through by 2:



Factor by grouping:









2)







Set first factor equal to zero:



Apply linear combination identity:



Setting yields for the interval given:



Set second factor equal to zero:



Apply linear combination identity:



Setting and yields for the given interval:

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March 4th, 2011, 10:01 PM   #3
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Correct.
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Could you generalize this, where n is any integer?
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March 4th, 2011, 10:18 PM   #4
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Re: Trigonometry

For problem 2, I should have put all the solutions together:



For problem 1, with no restriction on x, we could write the solutions for the two factors as:

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March 4th, 2011, 10:32 PM   #5
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My textbook's answer.
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March 7th, 2011, 05:04 AM   #6
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In that case, your textbook's answer is incorrect, since it omits some solutions.
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March 7th, 2011, 02:06 PM   #7
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I knew you were smarter than my textbook's solutions! Thanks for letting me know!
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