find the inclination angle

Question

Find the inclination (in radians and degrees) of the line with slope m.

m=-2

Answer 1

The slope -intercept form is y = mx + b m is slope and b is y intercept Here the given  slope m = -2 the slope - intercept is y = -2x + b  Slope = -2 m = -2 Re call m = tanθ, where θ is inclination angle m = tanθ = -2 θ = 1530 or  63o    Now in θ = radians θ = 153×3.14/180                  (simplify) θ = 0.255 radians Since the slope is positive Tangent sign should be positive, so the line passes through the I and III quadrant. So, inclination angle is 1530.

 

Comments

m = tan θ = -2

θ = tan^{- 1}(- 2) = - 63^o = tan^{- 1}(tan(180^o - 63^o)) = 117^o.

Now in θ = radians

θ = (117 × 3.14)/180

θ = 2.041radians..

Therefore, the inclination angle is 117⁰ (or) 2.041 radians.