Slope in between m and -1/m

maxpancho

How do I find a function of m to find this slope?

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HallsofIvy

MHF Helper
Since the slope is the tangent of the angle the line makes with the x-axis you will need some trig identities.

There is, for example, the sum law: $$\displaystyle tan(A+ B)= \frac{tan(A)+ tan(B)}{1+ tan(A)tan(B)}$$ as well as sin(A+ B)= sin(A)cos(B)- cos(A)sin(B) and cos(A+ B)= cos(A)cos(B)- sin(A)sin(B).

Also, $$\displaystyle tan(A/2)= \frac{1- cos(A)}{sin(A)}$$.

1 person

maxpancho

Trigonometry is a useful beast after all Thanks, HallsofIvy.

HallsofIvy

MHF Helper
As long as you keep in on a tight rein!