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March 7th, 2010, 12:47 PM   #1
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finding exact values of trig equations

I can find the exact values for simple equations like , but when they look like this I have a litte trouble.

I tried to solve the second one and i got 2pi/18 as a solution. It actually seemed to work, but I'm not sure if its right. Also once I find one solution how do I get the second solution.
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March 7th, 2010, 01:03 PM   #2
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Re: finding exact values of trig equations





We know that and equal 1/2 so you want to solve and for x.
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March 7th, 2010, 01:52 PM   #3
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Re: finding exact values of trig equations

Well I tried doing what you said and my two answers are


pi/18 and 9pi/18.

When I enter them in for x they equal 0 so I think they work.
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March 7th, 2010, 02:17 PM   #4
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Re: finding exact values of trig equations

Your solutions are correct. 9pi/18 is pi/2.
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March 7th, 2010, 02:43 PM   #5
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Re: finding exact values of trig equations

Ok thanks. In some of the problems I have instead of them being in radians they are in degrees and I don't know how this changes the way I should solve it.

For example,

3sec(4x+10degrees)=-9
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March 8th, 2010, 03:12 AM   #6
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Re: finding exact values of trig equations

cos(4x + 10) = -1/3
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March 8th, 2010, 08:00 AM   #7
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Re: finding exact values of trig equations

Quote:
Originally Posted by mtt0216
Ok thanks. In some of the problems I have instead of them being in radians they are in degrees and I don't know how this changes the way I should solve it.

For example,

3sec(4x+10degrees)=-9
If it's bad, you could always convert to radians. As a general rule, I work either completely in degrees or completely in radians, lest I err and forget the units of one. In general, I know trig values for radian measures better than degree measure. Just recall that 2pi radians = 360 degrees.
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March 8th, 2010, 10:18 AM   #8
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Re: finding exact values of trig equations

Quote:
Originally Posted by jason.spade
If it's bad, you could always convert to radians. As a general rule, I work either completely in degrees or completely in radians, lest I err and forget the units of one. In general, I know trig values for radian measures better than degree measure. Just recall that 2pi radians = 360 degrees.
That is sound advice. To learn a language, written or spoken, you have to learn to think in that language, and not continually translate back and forth. It comes with time, as with any spoken language.
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March 8th, 2010, 11:26 AM   #9
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Re: finding exact values of trig equations

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Originally Posted by greg1313
cos(4x + 10) = -1/3

When changing the equation from sec to cos what did you do to the -3 to change it to -1/3.
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March 8th, 2010, 11:37 AM   #10
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Re: finding exact values of trig equations

3sec(4x + 10) = -9
sec(4x + 10) = -3
1/cos(4x + 10) = -3
1 = -3cos(4x + 10)
-1/3 = cos(4x + 10)
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