January 16th, 2015, 08:23 PM  #1 
Member Joined: Dec 2014 From: Queensland Posts: 59 Thanks: 2  Simplify expression
Hi, I need to simplify the following. \(\cos\left(3π+α\right) \) I am unsure of the steps to take to do this. Thanks Last edited by skipjack; January 17th, 2015 at 08:40 PM. 
January 16th, 2015, 08:30 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351  Quote:
$\displaystyle \cos(x+y)=\cos{x}\cos{y}\sin{x}\sin{y}$ Last edited by skipjack; January 17th, 2015 at 08:41 PM.  
January 16th, 2015, 08:55 PM  #3 
Member Joined: Dec 2014 From: Queensland Posts: 59 Thanks: 2 
Sorry, I'm still unsure what you mean. Do you mean... \(\cos\left(3π+α\right)= \cos\left(3π\right)\cos\left(α\right)\sin\left(3π\right)\sin\left(α\right) \) ??? I'm behind as and an online student. Teacher and student interaction is at its minimum this semester. Haven't had a reply in my class forum for ages from the teacher. cou Last edited by skipjack; January 17th, 2015 at 08:43 PM. 
January 17th, 2015, 03:29 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,697 Thanks: 977 Math Focus: Elementary mathematics and beyond 
That's correct.

January 17th, 2015, 07:07 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,922 Thanks: 785 
Now, do you know what "" and "" are?
Last edited by greg1313; January 17th, 2015 at 12:33 PM. 
January 17th, 2015, 07:36 AM  #6 
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 175  Last edited by greg1313; January 17th, 2015 at 12:34 PM. 
January 17th, 2015, 02:36 PM  #7 
Member Joined: Dec 2014 From: Queensland Posts: 59 Thanks: 2 
I've been working with radians as well as degrees, so I assume \(3π\) would be the radian measure or \(540°\) but I don't need values. I'm looking on purplemaths website and I see the identity laws mentioned here. If I do \(\cos(3π)\sin(3π)=1 \) I still have \(\cos(α)\sin(α) \) would the answer be \(\cos(α) \) ? I still don't understand how I can simplify this further. Last edited by skipjack; January 17th, 2015 at 08:46 PM. 
January 17th, 2015, 03:00 PM  #8 
Math Team Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351 
$\displaystyle \cos(3\pi + \alpha) = \cos(3\pi)\cos(\alpha)  \sin(3\pi)\sin(\alpha)$ $\displaystyle \cos(3\pi + \alpha) = (1) \cdot \cos(\alpha)  (0) \cdot \sin(\alpha) = \cos(\alpha)$ 
January 17th, 2015, 04:23 PM  #9  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,662 Thanks: 652 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan Last edited by skipjack; January 17th, 2015 at 08:47 PM.  

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