Find the slopes of the lines which make the following angles with the

1.	Find the slopes of the lines which make the following angles with the positive direction of x - axis : \(\frac{2\pi}{3}\)
Answer» Given \(\frac{2\pi}{3}\) To Find: Slope of the line \(\frac{2\pi}{3}\) Angle made with the positive x - axis is The Slope of the line is m Formula Used: m = tanθ So, The slope of Line is m = tan \(\frac{2\pi}{3}\) ⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = tan \(\Big(\pi-\frac{\pi}{3}\Big)\) ⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = tan \(\Big(-\frac{\pi}{3}\Big)\) ⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = \(-\sqrt{3}\) Hence, The slope of the line is \(-\sqrt{3}\) .

Find the slopes of the lines which make the following angles with the positive direction of x - axis : \(\frac{2\pi}{3}\)

Answer»

Given \(\frac{2\pi}{3}\)

To Find: Slope of the line \(\frac{2\pi}{3}\)

Angle made with the positive x - axis is

The Slope of the line is m

Formula Used: m = tanθ

So, The slope of Line is m = tan \(\frac{2\pi}{3}\)

⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = tan \(\Big(\pi-\frac{\pi}{3}\Big)\)

⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = tan \(\Big(-\frac{\pi}{3}\Big)\)

⇒ tan \(\Big(\frac{2\pi}{3}\Big)\) = \(-\sqrt{3}\)

Hence, The slope of the line is \(-\sqrt{3}\) .