find the inclination angle

Question

Find the inclination (in radians and degrees) of the line passing through the points.

(1,2√3)(0,√3)

Answer 1

The slope - intercept form is y = mx + b, m is slope and b is y-intercept  The given points are (1,2√3)(0,√3) Slope formula is (y2-y1)/(x2-x1) Substitute the values in slope formula m = (√3 - 2√3)⁄(0 - 1)                            ((x1,y1)=(3,√3)and(x2,y2) = (6,-2√3)) m = (√3 - 2√3)⁄ - 1                                (Simplify ) m = -√3/-1 m =  √3 The slope intercept form is y = √3x + b Slope = √3 m =  √3 Re call m = tanθ, where θ is inclination angle m = tanθ = √3                                  θ = 600 or 150o now θ in radians   θ = 60×3.14/180                    (Simplify pi =3.14) θ = 1.04radians Since the slope is positive Tangent sign should be positive, so the line passes through the I and III quadrant. So, inclination angle is 600.

 

Comments

Therefore, the inclination angle is 60⁰ (or) 1.04 radians.