# Help with trig addition and subtraction formulas.

• December 4th 2011, 12:42 PM
dangsos
Help with trig addition and subtraction formulas.
If $sin (\alpha) = -\frac {5}{13}$ and $tan ( \alpha) > 0$ , find the exact value of $sin (\alpha - \frac{\pi}{3})$.

My first time using latex! Hopefully it makes my problem easier to read.

EDIT:
so the formula is sin(A-B)=(sinA)(cosB)-(cosA)(sinB)

I guess I should mention I know how to get every value except $cos(\alpha)$

and I don't understand why they are telling me $tan ( \alpha) > 0$
• December 4th 2011, 12:50 PM
dangsos
Re: Help with trig addition and subtraction formulas.
sin(A-B)=(sinA)(cosB)-(cosA)(sinB)

using this formula I get sin(A-B) = - $\frac{5}{13}$ * $\frac{\sqrt{3}}{2}$ - cos $(\alpha)$ * $\frac{1}{2}$
• December 4th 2011, 12:52 PM
Siron
Re: Help with trig addition and subtraction formulas.
You have given that $\tan(\alpha)>0$ i.e $\frac{\sin(\alpha)}{\cos(\alpha)}>0$
• December 4th 2011, 01:13 PM
dangsos
Re: Help with trig addition and subtraction formulas.
I don't understand. How does that help me find the missing peice $cos(\alpha)$ ?
• December 4th 2011, 01:18 PM
Siron
Re: Help with trig addition and subtraction formulas.
It means that $\cos(\alpha)<0$. I think it can be useful to use the identity $\cos(\alpha)=\pm \sqrt{1-\sin^2(\alpha)}$ (do you see the importance of $\cos(\alpha)<0$ now?)
• December 4th 2011, 01:20 PM
skeeter
Re: Help with trig addition and subtraction formulas.
Quote:

Originally Posted by dangsos
I don't understand. How does that help me find the missing peice $cos(\alpha)$ ?

it tells you what quadrant $\alpha$ is in ... lets you know whether to make $\cos{\alpha}$ positive or negative.
• December 4th 2011, 01:33 PM
dangsos
Re: Help with trig addition and subtraction formulas.
so using $\sqrt{1-sin^2(\alpha)}$ i get cos $(\alpha) = -\sqrt{\frac{144}{169}}$ correct?
• December 4th 2011, 01:36 PM
Siron
Re: Help with trig addition and subtraction formulas.
Normally it has to be $\frac{-12}{13}$
I think you can solve the exercice now ...
• December 4th 2011, 01:45 PM
dangsos
Re: Help with trig addition and subtraction formulas.
okay so with all that I get this

sin(A-B) = $- \frac{5}{13} * \frac{\sqrt{3}}{2} - ( \frac{12}{13}) * \frac{1}{2}$

my answer is $- \frac{5 * \sqrt{3} - 12}{26}$
the book gives $\frac{12 * \sqrt{3} - 5}{26}$
• December 4th 2011, 01:52 PM
skeeter
Re: Help with trig addition and subtraction formulas.
$\sin{\alpha} \cdot \cos{\frac{\pi}{3}} - \cos{\alpha} \cdot \sin{\frac{\pi}{3}} =$

$-\frac{5}{13} \cdot \frac{1}{2} - \left(-\frac{12}{13}\right) \cdot \frac{\sqrt{3}}{2}$

try again ...
• December 4th 2011, 02:10 PM
dangsos
Re: Help with trig addition and subtraction formulas.
I always make the most simple mistakes >.< thank yo ufor correcting me.