Question

@michele_laino @welshfella

Answer 1

@Michele_Laino

Answer 2

here is the first hint:
\[\begin{gathered}
\tan \left( {\frac{{5\pi }}{6}} \right) = \tan \left( {\pi - \frac{\pi }{6}} \right) = \hfill \\
\hfill \\
= \frac{{\tan \pi - \tan \left( {\pi /6} \right)}}{{1 + \tan \pi \cdot \tan \left( {\pi /6} \right)}} = ...? \hfill \\
\end{gathered} \]

Answer 3

and the second hint (without calculator):
\[\begin{gathered}
\tan \left( { - \frac{{11\pi }}{6}} \right) = \tan \left( {\frac{\pi }{6} - 2\pi } \right) = \hfill \\
\hfill \\
= = \frac{{\tan \left( {\pi /6} \right) - \tan \left( {2\pi } \right)}}{{1 + \tan \left( {2\pi } \right) \cdot \tan \left( {\pi /6} \right)}} = ...? \hfill \\
\end{gathered} \]

Answer 4

With the second one, from the numbers that I put in I got \[\sqrt{3}/3\]

Answer 5

ok!

Answer 6

Is that correct?

Answer 7

yes! the second one is correct!

Answer 8

With the first one, I got \[-\sqrt{3}\]

Answer 9

I got a different result

Answer 10

I think my calculations were wrong, let me re-input them.

Answer 11

hint:
please, keep in mind this value:
\[\tan \left( {\pi /6} \right) = \frac{1}{{\sqrt 3 }}\]

Answer 12

Is it \[\sqrt{3}\]

Answer 13

I think it isn't correct

Answer 14

\[-\sqrt{3}/3\]

Answer 15

that's right!

Answer 16

Thank you! Could you help me with another question please?

Answer 17

ok!

Answer 18

at \theta=0, we have cos(2 \theta)=2

Answer 19

When I attempted this question, I think I got graph B as the answer, but I think I'm wrong.

Answer 20

more correctly, \[2\cos \left( {2\theta } \right) = 2,\quad if\;\theta = 0\]

Answer 21

So, not B?

Answer 22

please note that:
\[2\cos \left( {2\theta } \right) = 2,\quad if\;\theta = \pi \]

Answer 23

C!?

Answer 24

that's right!

Answer 25

Could you help me with another question please?(:

Answer 26

I'm sorry, I have to go to dinner

Answer 27

It'll be quick though, please???

Answer 28

ok!

Answer 29

Is the correct answer D? I'm not guessing, I really think its D, but I'm not sure.

Answer 30

here, we have to keep in mid that:
\[\begin{gathered}
\tan \left( {\frac{{4\theta }}{3}} \right) = 0,\quad if\;\theta = 0 \hfill \\
\hfill \\
\tan \left( {\frac{{4\theta }}{3}} \right) = + \infty ,\quad if\;\theta = \frac{{3\pi }}{8} \hfill \\
\end{gathered} \]

Answer 31

B!?

Answer 32

yes! I think so

Answer 33

Can you help me with one more question please? Its the last one and it'll be quick I promise please?

Answer 34

I'm very sorry, I have to go to dinner :(

Answer 35

Okay, thank you very much!

Answer 36

:)