Question

tan(-4pi/3) find the value.​

Answer 1

tan is positive in 3rd quadrant

hope so it may help you

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Answer 2

Answer :-

${\boxed{\sf{\implies Value\; of \; \tan \frac{ -4 \pi}{3} \; is \; - \sqrt{3} }}}$

Solution :-

$\sf{\implies \tan \frac{-4 \pi }{3} = - \tan \frac{4 \pi }{3} }$

⊕ Except cos and sec theta every other trignometric angle having negative angle negative sign comes out .

Now we'll break the angle

$\sf{\implies \frac{4 \pi }{3} = \pi + \frac{\pi}{3}}$

$\sf{\implies \tan (\frac{-4 \pi }{3} ) =\; - \tan (\pi + \frac{\pi}{3} )}$

π + Ф = the angle will lie in thirg quadrant .

We know that tan Ф is positive in 3rd quadrant . So our angle will remain the same .

$\sf{\implies - \tan \frac{4 \pi }{3 } = - \tan \frac{\pi}{3} }$

Value of tan 60° = $\sf{\sqrt{3}}$

$\implies - \tan( \frac{\pi}{3} ) = - \sqrt{3} }$

${\underline{\underline{\sf{So \; answer\; is \; - \sqrt{3} }}}}$

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Some extra information

⇔In 1st quadrant = All angles are positive .

⇔In 2nd quadrant = Sine and Cosec are positive .

⇔In 2nd quadrant = Tan and Cot are positive .

⇔In 4th quadrant = Cos and Sec are positive .