Question

find the slope of a line whose inclination to xaxis is 2pie/3​

Answer 1

Answer:

Slope =-√3

Step-by-step explanation:

Given that:-

the slope of a line whose inclination to xaxis is 2pie/3

=>2π/3

=>2(180)/3

=>2(60)

=>120°

Angle =120°

we know that

The slope of the line whose inclination to x-axis θ=m=tanθ

=>m=tan 120°

=>m=tan(90+30°)

we know that tan (90+ θ)=-cot θ

=>m=-cot30°

=>m=- √3

Slope =-√3

Answer 2

$\mathfrak{\huge \underline{Question:}}$

find the slope of a line whose inclination to xaxis is 2π/3

$\mathfrak{\huge \underline{Solution:}}$

$\sf Slope = tan \theta \\\\\sf tan \frac{2 \pi} {3}= \frac{sin\frac{2 \pi}{3}} {cos\frac{2 \pi} {3}} \\\\\sf tan \frac{2 \pi} {3}= \frac{sin\frac{2 \pi} {3}} {cos\frac{2 \pi} {3}} \\\\\sf =tan \frac{2 \pi} {3}= \frac{\frac{\sqrt{3}}{2}} {\frac{-1}{2}} = - \sqrt{3}$