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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Solution

The slope m of a line making an angle θ with the positive direction of x axis in anticlockwise direction is given by,

m=tan θ 1 (1)

Let θ 1 be the angle subtended by the line with the positive direction ofx-axis in anticlockwise direction.

The angle made by the line with the positive direction ofx-axis in anticlockwise direction is,

θ 1 =90°+30° =120°

Substitute the value of θ 1 as 120° in equation (1).

m=tan120° =tan( 90°+30° ) =−cot( 30° ) =− 3

Thus, the slope of the line makes an angle of 30° with the positive direction ofy-axis in anticlockwise direction. is − 3 .

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