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Angle x-axis and straight line

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
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2 Answers

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
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.

Comments

149.04º or 2.6 radians is correct since the question as for the angle wrt the positive x-axis.