Angle x-axis and straight line

Question

The angle which the straight line 3x +5y+2=0 makes with the positive direction of the x-axis is closest to?

Full working if possible.

Thanks in advance

Answer 1

I think that in this case the sign indicates that the angle is not in the first quadrant, it may be in the second quadrant or in the fourth quadrant where the function sin and cos have different signs.

The procedure is correct but the angles may be:

-30.964 and also 149.04 degrees measured from the origin.

Answer 2

Hello Tiarne,

 

To find the angle that this equation forms with the x-axis, we must first find the slope.

 

3x +5y+2=0

5y=-3x-2

y=(-3/5)x-2/5

 

Slope is -3/5.  To find the angle of this slope consider the definitions of tangent:

tan(θ) = opp/adj = sin(θ)/cos(θ)

 

Tangent is the vertical component divided by the horizontal component, aka  rise over run, aka the slope.  So we can say:

 

tan(θ)=(-3/5)

tan^-1(-3/5)=θ

θ≈-30.964°

or θ≈-.5404 radians