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!!
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Verified answer
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
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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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