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equation of a stright line passing through the origin and making with x-axis an angle twice the size of the angle made by the line y=0.2x with x-axis, is:



10-Oct-2015 12:06 PM
~14

Answers (1)


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Since the line passes through the origin, its equation will be like: y = mx

(m = slope of the line)

Angle made by line y = 0.2x will be tan-10.2.

Angle made by required line = twice of above angle = 2tan-10.2

Slope of our line = tan(theta) = tan(2tan-10.2).

Using the property tan2x = 2tanx / (1 - tan2x):

slope = 2tan(tan-10.2) / (1- tan2(tan-10.2) )

Now using the property: tan(tan-1x) = x.

slope = 2(0.2) / (1 - 0.22)

         = 0.4 / 0.96

        = 0.416

Therefore, Equation of our required line: y = 0.416x



10-10-2015 12:39
~32

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