Function: math[lineangle] - angle between two curves in the plane

Calling Sequence:

lineangle(f);
lineangle(f, x, options);
lineangle(f, x=a, options);

Parameters:

f - any expression in x or a list of two expressions in x
x - a name
a -
a point (numerical or symbolic value)

options - one or two options ('floats' or 'degrees')

Description:

This function determines the angle between two curves in the plane (graphs of real-valued functions in one indeterminate x).

If f is is just one expression, lineangle evaluates the angle between the function f and the x-axis (g(x)=0). To determine the angle between two given functions, they must be included in a list.

If f is either a constant or linear function and if it contains only the name x, the first or second form may be used. The same applies if the list f contains only constant or linear functions.

If f (or the expressions in the list f) include(s) more than one name (e.g. one or more parameters), the indeterminate must be given as the second argument to lineangle.

If f is not a constant or linear function, the point x=a must be specified. Alternatively if the list f contains at least one non-constant or non-linear function, the point must be given, as well.

By default, the result is returned in radians. Use option 'degrees' in order to evaluate the angle of intersection in degrees.

One further option is 'floats' or 'float' which returns the result as a floating-point number. This option can be combined with option 'degree' in any order.

A shortcut to lineangle is 'langle'.

Internally lineangle uses the function math/slopefn to determine the slope m1 of the function f or the slopes m1, m2 of the two functions contained in the list f. If m1*m2 = -1, i.e. the curves are orthogonal, lineangle returns Pi/2.

This function is part of the math package, and so can be used only after performing the command with(math) or with(math, lineangle).

Examples:

> with(math, lineangle):

> lineangle([2*x-3, 1/2*x+1]);

[Maple Math]

> lineangle([5*x+7, 2/3*x+1/3], x, floats);

[Maple Math]

> lineangle([-1/2*x, 2*x], x, degrees);

[Maple Math]

> r1 := rhs(isolate(x/a+y/b=1, y));

[Maple Math]

> r2 := rhs(isolate(x/b+y/a=1, y));

[Maple Math]

> lineangle([r1, r2], x);

[Maple Math]

> lineangle(x, x=1, degrees);

[Maple Math]

> lineangle(x^2, x=1, degrees, floats);

[Maple Math]

See Also:

math/tangente , math/normale , math/slopefn , math/curveplot .

Version History:

Version 1.0 as of December 07, 1997.