質問編集履歴
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実現したい事の説明の改善をしました．
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関数z(x)を微分して法線を求め，その法線の傾き値（度表記）を求めようとしています．
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また，傾き値は
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また，傾き値はその座標値(a,z(a))の値で変化すると思いますが，aが0.1間隔で0から6まで変化した分だけの情報（すばわち60個分の傾き値）が欲しいです．
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下図がイメージです．
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編集後 のところに訂正して頂いたプログラムを基に，作成したプログラムを載せました．しかし，エラーが出てしまいます．．．
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# 編集後
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```Python
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#法線の角度を求める
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import matplotlib.pyplot as plt
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import numpy as np
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from sympy import *
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from sympy import Derivative, Symbol, N
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# xを変数xに指定
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x = Symbol('x')
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z = -(c*x**2/(1+(1-(1+k)*c**2*x**2)**(1/2))
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prime_z = Derivative(z, x).doit()
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a = Symbol('a')
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z_a = z.subs(x, a) # f(a)
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prime_z_a = prime_z.subs(x, a) # 点 (a, f(a)) の傾き
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tangent = prime_z_a * (x - a) + z_a # 点 (a, f(a)) の接線
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normal = (-1 / prime_z_a) * (x - a) + z_a # 点 (a, f(a)) の法線
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theta = deg(atan(-1 / prime_z_a)) # 法線の角度
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print('{} degree'.format(theta.evalf(subs={a: x, prime_z_a: x})))
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# x, theta の点一覧を作成する。
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xs = np.arange(0, 6.28, 0.1)
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thetas = [theta.evalf(subs={x: v}) for v in xs]
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#
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# 描画する。
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fig, ax = plt.subplots(figsize=(7, 7))
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plt.grid(True)
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plt.xlabel('$x$', fontsize=16)
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plt.ylabel('$θ$', fontsize=16)
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plt.title('upper die')
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plt.plot(xs, thetas)
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plt.show()
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np.savetxt("points.csv", np.vstack([xs,thetas]).T, delimiter=",")
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```
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を入力すると，
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```
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>>> # 描画する。
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... fig, ax = plt.subplots(figsize=(7, 7))
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>>> plt.grid(True)
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>>> plt.xlabel('$x$', fontsize=16)
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Text(0.5,0,'$x$')
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>>> plt.ylabel('$θ$', fontsize=16)
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Text(0,0.5,'$\x83\xc6$')
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>>> plt.title('upper die')
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Text(0.5,1,'upper die')
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>>> plt.plot(xs, thetas)
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Traceback (most recent call last):
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File "<stdin>", line 1, in <module>
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\pyplot.py", line 3363, in plot
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ret = ax.plot(*args, **kwargs)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\__init__.py", line 1867, in inner
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return func(ax, *args, **kwargs)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\axes\_axes.py", line 1529, in plot
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self.add_line(line)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\axes\_base.py", line 1960, in add_line
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self._update_line_limits(line)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\axes\_base.py", line 1982, in _update_line_limits
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path = line.get_path()
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\lines.py", line 956, in get_path
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self.recache()
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\lines.py", line 657, in recache
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y = _to_unmasked_float_array(yconv).ravel()
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\matplotlib\cbook\__init__.py", line 2052, in _to_unmasked_float_array
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return np.asarray(x, float)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\numpy\core\numeric.py", line 501, in asarray
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return array(a, dtype, copy=False, order=order)
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File "C:\Users\owner\Anaconda3\envs\python3.6\lib\site-packages\sympy\core\expr.py", line 225, in __float__
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raise TypeError("can't convert expression to float")
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TypeError: can't convert expression to float
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>>> plt.show()
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```
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この様なエラーが出てしまいます．
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