Question

Radians:
What is the exact value of tan 5/3 pi

Answer 1

\[\tan 5\div3 \pi \]

Answer 2

can you please show the working out :)

Answer 3

The tangent has period pi, this means you can add or subtract pi from the angle as many times as you like, the tangent remains the same, or:

\[\tan \frac{ 5 }{ 3 }\pi = \tan \left( \frac{ 5 }{ 3 }\pi -2\pi \right) = \tan \left( -\frac{ 1 }{ 3 } \pi\right) \]

Now you can place the minus sign in front of the tan, because it is an uneven function.
This means that for every x: tan(-x) = -tanx, so:

\[\tan \left( -\frac{ 1 }{ 3 }\pi \right) = -\tan \left( \frac{ 1 }{ 3 } \pi\right)\]

Now the hardest part ;) : Aren't you supposed to learn by heart som special values of sin, cos and tan?
Well, if you are, you now remember that\[\tan \left( \frac{ 1 }{ 3 }\pi \right) = \sqrt{3}\]
So the answer is \[-\sqrt{3}\]

Hope this helps!

ZeHanz

Answer 4

You are the best thank you