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Find the inclination (in radians and degrees) of the line with slope m=-1

+1 vote
please help!!!!!!
asked Dec 21, 2012 in GEOMETRY by Justin Pupil

1 Answer

+2 votes

Here the given slope is m = -1

The slope equation is    y =mx + b

                                            y = (-1)x + b

           Inclination angle   m = tan θ

                   therefore  tanθ = -1

                                tanθ = tan 135°

                                θ = 135° or 135 × 3.14/180 = 2.355

So, here the inclination angle is θ = 135°  or   2.355 radians

answered Dec 22, 2012 by ricky Pupil
reshown Dec 23, 2012 by moderator

The function tan (θ) is negative in second and fourth quadrant.

tan (θ) = - 1.

In second Quadrant, π/2θπ.

- 1 = tan (- π/4) = tan ( π - π/4) = tan (3π/4).

In fourth Quadrant, 3π/2θ ≤ 2π.

- 1 = tan (- π/4) = tan ( - π/4) = tan (7π/4).

The solutions are θ = 3π/4 and θ = 7π/4.

So, the inclination angles are θ = 3π/4 radians or θ = 135°and θ = 7π/4 radians or θ = 315°.

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