## anonymous one year ago How do you find cos(11pi/6)?

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1. misty1212

HI!!

2. misty1212

you need a good trig cheat sheet !

3. Michele_Laino

hint: we have: $\Large \frac{{11\pi }}{6} = 2\pi - \frac{\pi }{6}$

4. misty1212

5. Michele_Laino

so we can write: $\Large \cos \left( {\frac{{11\pi }}{6}} \right) = \cos \left( {2\pi - \frac{\pi }{6}} \right)$

6. misty1212

find $$\frac{11\pi}{6}$$ on the unit circle on the the last page of the cheat sheet, then look at the coordinates of the corresponding point the first coordinate is cosine

7. anonymous

Thanks guys

8. misty1212

$\color\magenta\heartsuit$

9. anonymous

What if you need to find tangent?

10. Michele_Laino

you can apply this identity: $\Large \begin{gathered} \tan \left( {\frac{{11\pi }}{6}} \right) = \tan \left( {2\pi - \frac{\pi }{6}} \right) = \hfill \\ \hfill \\ = \frac{{\tan \left( {2\pi } \right) - \tan \left( {\frac{\pi }{6}} \right)}}{{1 + \tan \left( {2\pi } \right)\tan \left( {\frac{\pi }{6}} \right)}} \hfill \\ \end{gathered}$

11. anonymous

How do you know tan(11pi/6) equals tan(2pi-pi/6)?