MaplePrimes - answers and comments on Question, Create a tangent function

Re

Kitonum — Sun, 13 Jan 2013 00:27:27 Z

To the 1st question:

restart;

f:=x->piecewise((x>=0.19740 and x<0.91510) or (x>=3.3390 and x<4.0567), tan(x), undefined);

plot(f(x), view=[-1..5, -0.5..1.5], scaling=constrained);

To the 2nd question:

restart;

solve({ 0.2 <= tan(x), tan(x)< 1.3, x>0, x<Pi});

plot(tan(x), x=lhs(%[1])..rhs(%[2]));

Explanation

Markiyan Hirnyk — Sun, 13 Jan 2013 00:37:03 Z

As far as I understand it, the command
> solve({.2 < tan(x), tan(x) < 1.3});

            {-2.944197094 < x, x < -2.226491953}, {0.1973955598 < x, x < 0.9151007006},
              {3.338988213 < x, x < 4.056693354}
produces only solutions belonging to RealRange(-Pi,2*Pi).The allsolutions option does not
work here. If you want to obtain all solutions belonging to RealRange(a,b),
then you should use the command
> solve({.2 < tan(x), tan(x) < 1.3,x>a,x <b}). For example,
> solve({x > -10*Pi, .2 < tan(x), x < -Pi, tan(x) < 1.3});

            {-31.21853098 < x, x < -30.50082584}, {-28.07693832 < x, x < -27.35923318},
              {-24.93534567 < x, x < -24.21764053}, {-21.79375302 < x, x < -21.07604787},
              {-18.65216036 < x, x < -17.93445522},{-15.51056771 < x, x < -14.79286257},
              {-12.36897505 < x, x < -11.65126991},{-9.227382401 < x, x < -8.509677260},
              {-6.085789747 < x, x < -5.368084607}

> sol := solve({x > -10*Pi, .2 < tan(x), x < 20*Pi, tan(x) < 1.3}, [x]);
> nops(sol);
                               30
> plot([tan(x), .2, 1.3], x = -10*Pi .. -Pi, discont = true);

Thank you so much for the answer. But do

khalijefars — Sun, 13 Jan 2013 00:37:32 Z

Thank you so much for the answer. But do you know whether it is possible to do it like the picture?

this pic is not from the exercise but an example

khalijefars — Sun, 13 Jan 2013 00:38:14 Z

this pic is not from the exercise but an example

How about this?

Markiyan Hirnyk — Sun, 13 Jan 2013 00:49:28 Z

> with(plots): a := implicitplot(max(.2-tan(x), tan(x)-1.3, -Pi-x, x-2*Pi, y-tan(x), -y) <= 0, x = -Pi .. 2*Pi, y = 0 .. 5, numpoints = 10^5, filled = true);
> b := plot([tan(x), .2, 1.3], x = -Pi .. 2*Pi, discont = true);
> display([a, b]);

See ?plots for more details.

Wonderful!!!!! A lot of thanks!

khalijefars — Sun, 13 Jan 2013 00:50:37 Z

Wonderful!!!!! A lot of thanks!