Help me on this question..........

Mathematics

1 answer:

aleksandrvk [35]3 years ago

7 0

Answer: $18

Explanation: 6x3

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4pi/3 find the exact trigonometric ratios for the angle whose radian measue is given

bulgar [2K]

Answer:

All trigonometric ratios.

Step-by-step explanation:

We have to find all the trigonometric ratios.

Given:

$\theta = \dfrac{4\pi}{3} = \pi + \dfrac{\pi}{3}$

Formula:

$\sin(\pi +x) = -\sin(x)\\\cos(\pi +x) = -\cos(x)$

$\sin(\pi + \dfrac{\pi}{3}) = -\sin(\dfrac{\pi}{3}) = -\dfrac{\sqrt{3}}{2}$

$\cos ((\pi + \dfrac{\pi}{3})) = -\cos(\dfrac{\pi}{3}) = -\dfrac{1}{2}$

Formula:

$\tan\theta =\dfrac{\sin\theta}{\cos\theta}\\\cot\theta = \dfrac{1}{\tan\theta}\\\sec\theta = \dfrac{1}{\cos\theta}\\\csc\theta = \dfrac{1}{\sin\theta}$

$\tan(\pi + \dfrac{\pi}{3})= \dfrac{\sin(\pi + \dfrac{\pi}{3})}{\cos(\pi + \dfrac{\pi}{3})}\\\\\tan(\pi + \dfrac{\pi}{3}) = \dfrac{\frac{-\sqrt{3}}{2}}{\frac{-1}{2}} = \sqrt{3}$