Maths homework help (A level maths, core 3)?

May 2021 2 35 Report

Maths homework help (A level maths, core 3)?

The line l with equation y=(3/4)x bisects the angle between the x axis and the line y=mx

m>0

Given that the scales on each axis are the same, and that l makes an angle x with the x axis...

A) Write down the value of tanx

B) Showt hat m = 24/7

(Please show working/explain)

THANKS!!

The line (l)-----

y=(3/4)x

Indicates that the line is inlined at an angle of Tan⁻¹ (3/4) degrees with the x-axis. ie = 36.87 degree

Hence according to the given data , the line y = m x must be inclined at an angle 2 [Tan⁻¹ (3/4) ] with the x-axis. ie = 73.74 degree

That is m = Tan [ 73.74 ] = 3.428 = 24/7 ............ Answer Answer

....................................................................

SECOND METHOD

Note : it is given that " the scales on each axis are the same, and that l makes an angle ( θ ) with the x axis... "

Now consider the line (l) y = (3/4) x

Clearly Tan θ = (3/4)

As per the given condition, the line y = mx makes an angle ( 2 θ ) with the x-axis. Hence its m = tan 2 θ

.......................... 2 tan θ

=> m = tan 2 θ = --------------------

......................... 1 -- tan² θ

=> m = 2 ( 3/4 ) / [ 1 -- ( 3/4)² ] = 24/7 .... Answer Answer

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