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 unistu January 16th, 2015 08:23 PM

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

 skeeter January 16th, 2015 08:30 PM

Quote:
 Originally Posted by unistu (Post 218971) Hi, I need to simplify the following. $$\cos\left(3π+α\right)$$ I am unsure of the steps to take to do this. Thanks
Use the sum identity for cosine ...

$\displaystyle \cos(x+y)=\cos{x}\cos{y}-\sin{x}\sin{y}$

 unistu January 16th, 2015 08:55 PM

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

 greg1313 January 17th, 2015 03:29 AM

That's correct.

 Country Boy January 17th, 2015 07:07 AM

Now, do you know what "$cos(3\pi)$" and "$sin(3\pi)$" are?

 aurel5 January 17th, 2015 07:36 AM

Quote:
 Originally Posted by Country Boy (Post 219022) "$cos(3\pi)$" and "$sin(3\pi)$"
$\displaystyle \cos 3\pi$

 unistu January 17th, 2015 02:36 PM

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.

 skeeter January 17th, 2015 03:00 PM

$\displaystyle \cos(3\pi + \alpha) = \cos(3\pi)\cos(\alpha) - \sin(3\pi)\sin(\alpha)$

$\displaystyle \cos(3\pi + \alpha) = (-1) \cdot \cos(\alpha) - (0) \cdot \sin(\alpha) = -\cos(\alpha)$

 topsquark January 17th, 2015 04:23 PM

Quote:
 Originally Posted by unistu (Post 219064) 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.
You are, I hope, aware that $\displaystyle \cos(3 \pi ) = \cos(2 \pi + \pi ) = \cos(\pi)$? (In degrees this is $\displaystyle \cos(540^\circ) = \cos( 360^\circ + 180^\circ ) = \cos(180^\circ)$.)

-Dan

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