Find the slope of the line- which makes an angle of 30- with the positive direction of y - axis measured anticlockwise-

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Standard XI

Mathematics

Allied Angles

Find the slop...

Question

Find the slope of the line, which makes an angle of $30^{\circ}$ with the positive direction of y - axis measured anticlockwise.

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Solution

The line makes an angle of $30^{\circ}$ with the positive direction of y-axis.

Now the line makes an angle of $(90 + 30)^{\circ} = 120^{\circ}$ with the positive direction of x - axis.

$∴$ Slope of the line = $t a n 120^{\circ} = t a n (90 + 30)$

$= - c o t 30^{\circ} = - \sqrt{3}$

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

The line makes an angle of 30∘ with the positive direction of y-axis. Now the line makes an angle of (90+30)∘=120∘ with the positive direction of x - axis. ∴ Slope of the line = tan 120∘=tan(90+30) =−cot 30∘=−√3

Find the slope of the line, which makes an angle of $30^{\circ}$ with the positive direction of y - axis measured anticlockwise.

The line makes an angle of $30^{\circ}$ with the positive direction of y-axis.

Now the line makes an angle of $(90 + 30)^{\circ} = 120^{\circ}$ with the positive direction of x - axis.

$∴$ Slope of the line = $t a n 120^{\circ} = t a n (90 + 30)$

$= - c o t 30^{\circ} = - \sqrt{3}$