> `assign`(p, convert(series(sin(z), z, 14), polynom)); 1
 

`assign`(p, `+`(z, `-`(`*`(`/`(1, 6), `*`(`^`(z, 3)))), `*`(`/`(1, 120), `*`(`^`(z, 5))), `-`(`*`(`/`(1, 5040), `*`(`^`(z, 7)))), `*`(`/`(1, 362880), `*`(`^`(z, 9))), `-`(`*`(`/`(1, 39916800), `*`(`^`... (1)
 

> `assign`(B, map(abs, p)); 1
 

`assign`(B, `+`(abs(z), `*`(`/`(1, 6), `*`(`^`(abs(z), 3))), `*`(`/`(1, 120), `*`(`^`(abs(z), 5))), `*`(`/`(1, 5040), `*`(`^`(abs(z), 7))), `*`(`/`(1, 362880), `*`(`^`(abs(z), 9))), `*`(`/`(1, 3991680... (2)
 

> plots[logplot](`/`(`*`(B), `*`(abs(p))), z = `+`(`-`(`*`(1.5, `*`(Pi)))) .. `+`(`*`(1.5, `*`(Pi))), colour = BLACK)
 

Plot_2d
 

> `/`(`*`(`^`(`+`(`*`(1.5, `*`(evalf(Pi)))), 15)), `*`(factorial(15)))
 

0.9596599399e-2 (3)
 

> `assign`(Order, 14); 1
 

`assign`(Order, 14) (4)
 

> with(numapprox); 1
 

[chebdeg, chebmult, chebpade, chebsort, chebyshev, confracform, hermite_pade, hornerform, infnorm, laurent, minimax, pade, remez]
[chebdeg, chebmult, chebpade, chebsort, chebyshev, confracform, hermite_pade, hornerform, infnorm, laurent, minimax, pade, remez]
(5)
 

> `assign`(pc, chebyshev(sin(`*`(`+`(`*`(3, `*`(Pi, `*`(z)))), `/`(1, 2))), z, 0.10e-4)); 1
 

`assign`(pc, `+`(`-`(`*`(.563315817501039, `*`(T(1, z)))), `-`(`*`(.811712834636678, `*`(T(3, z)))), `*`(.446025508330773, `*`(T(5, z))), `-`(`*`(0.775980406180141e-1, `*`(T(7, z)))), `*`(0.6975393014...
`assign`(pc, `+`(`-`(`*`(.563315817501039, `*`(T(1, z)))), `-`(`*`(.811712834636678, `*`(T(3, z)))), `*`(.446025508330773, `*`(T(5, z))), `-`(`*`(0.775980406180141e-1, `*`(T(7, z)))), `*`(0.6975393014...
`assign`(pc, `+`(`-`(`*`(.563315817501039, `*`(T(1, z)))), `-`(`*`(.811712834636678, `*`(T(3, z)))), `*`(.446025508330773, `*`(T(5, z))), `-`(`*`(0.775980406180141e-1, `*`(T(7, z)))), `*`(0.6975393014...
(6)
 

> `assign`(Bc, map(abs, %))
 

`assign`(Bc, `+`(`*`(.563315817501039, `*`(abs(T(1, z)))), `*`(.811712834636678, `*`(abs(T(3, z)))), `*`(.446025508330773, `*`(abs(T(5, z)))), `*`(0.775980406180141e-1, `*`(abs(T(7, z)))), `*`(0.69753...
`assign`(Bc, `+`(`*`(.563315817501039, `*`(abs(T(1, z)))), `*`(.811712834636678, `*`(abs(T(3, z)))), `*`(.446025508330773, `*`(abs(T(5, z)))), `*`(0.775980406180141e-1, `*`(abs(T(7, z)))), `*`(0.69753...
`assign`(Bc, `+`(`*`(.563315817501039, `*`(abs(T(1, z)))), `*`(.811712834636678, `*`(abs(T(3, z)))), `*`(.446025508330773, `*`(abs(T(5, z)))), `*`(0.775980406180141e-1, `*`(abs(T(7, z)))), `*`(0.69753...
(7)
 

> plot(eval(Bc, T = ChebyshevT), z = -1 .. 1)
 

Plot_2d
 

> plots[logplot](eval(`/`(`*`(Bc), `*`(abs(pc))), T = ChebyshevT), z = -1 .. 1, colour = BLACK)
 

Plot_2d
 

>