Determine the equation of the straight bisector of the acute angle that the straight form with the axis .
I have never done a problem like this but I will give it a try.
The angle between the x-axis and y=2x is
atan(opp/adj)=atan(rise/run)=atan(m)=atan(2)=1.1071 radians
The bisector of an angle make half this angle with the x-axis, so .55355 radians
tan(.55355) = opp/adj = rise/run = m2 = .6180
So I think the formula for a bisector is y=.6180*x or y=(tan(atan(angle)/2))*x
Hello, Apprentice123!
We can solve this without a calculator
. . which is what they probably expected.
Determine the equation of the bisector of the acute angle
formed by the straight line and the -axis.Code:| A | / B | / * | / * | / ½θ * | / * |/ * ½θ O * - - - - - - - X |
Line has the equation: .
. . Let
Its slope is: .
We want: .
Since , is in a right triangle with:
And Pythagorus tell us that: .
. . Hence: .
We have: . .
Rationalize: .
Therefore, the equation of the bisector is: .