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 March 7th, 2010, 12:47 PM #1 Newbie   Joined: Mar 2010 Posts: 16 Thanks: 0 finding exact values of trig equations I can find the exact values for simple equations like $-2sinx=\sqrt{2}$, but when they look like this $2cos(3x+\pi/6)-1=0$ 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.
 March 7th, 2010, 01:03 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: finding exact values of trig equations $2\cos{(3x\,+\.\pi /6)}\,-\,1\,=\,0$ $\cos{(3x\,+\.\pi /6)}\,=\,\frac{1}{2}$ We know that $\cos{(\pi/3)}$ and $\cos{(\frac{5\pi}{3})}$ equal 1/2 so you want to solve $3x\,+\,\pi/6\,=\,\pi/3$ and $3x\,+\,\pi/6\,=\,\5\pi/3$ for x.
 March 7th, 2010, 01:52 PM #3 Newbie   Joined: Mar 2010 Posts: 16 Thanks: 0 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.
 March 7th, 2010, 02:17 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: finding exact values of trig equations Your solutions are correct. 9pi/18 is pi/2.
 March 7th, 2010, 02:43 PM #5 Newbie   Joined: Mar 2010 Posts: 16 Thanks: 0 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
 March 8th, 2010, 03:12 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: finding exact values of trig equations cos(4x + 10) = -1/3
March 8th, 2010, 08:00 AM   #7
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Re: finding exact values of trig equations

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 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.

March 8th, 2010, 10:18 AM   #8
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Re: finding exact values of trig equations

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 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.

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.

 March 8th, 2010, 11:37 AM #10 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 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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