Find the slope of the line, which makes an angle of $30^{o}$ with the positive direction of $y - a x i s$ measured anticlockwise.

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Solution

REF.Image
The line make angle of $30^{\circ}$ from positive y axis
Hence it make angle of $(90^{\circ} + 30^{\circ})$ from positive x axis, i.e, $120^{\circ}$ from positive x axis
Hence $θ = 120^{\circ}$
Slope = $m = t a n θ = a t n 120^{\circ} = t a n (180 - 60^{\circ}) = t a n 60^{\circ} = - \sqrt{3}$
Slope of line = $- \sqrt{3}$

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Find the slope of the line, which makes an angle of 30o with the positive direction of y−axis measured anticlockwise.

REF.ImageThe line make angle of 30∘ from positive y axisHence it make angle of (90∘+30∘) from positive x axis, i.e, 120∘ from positive x axis Hence θ=120∘Slope = m=tanθ=atn120∘=tan(180−60∘)=tan60∘=−√3Slope of line = −√3

Find the slope of the line, which makes an angle of $30^{o}$ with the positive direction of $y - a x i s$ measured anticlockwise.