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{"cells":[{"cell_type":"markdown","metadata":{"id":"jAMKoELNpsK-"},"source":["<center><h1><b>Numerical Values of Trigs\n","</h1></b>\n","\n","Dr. Bingsen Wang\n","\n","12/21/2023\n","</center>"]},{"cell_type":"markdown","metadata":{"id":"Hv0YxDrWU4h8"},"source":["#Python Code\n","The Python code illustrates the Numerical Values of trigonometries."]},{"cell_type":"code","execution_count":121,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":745},"executionInfo":{"elapsed":413130,"status":"ok","timestamp":1703177247241,"user":{"displayName":"Bingsen Wang","userId":"15935430531228143675"},"user_tz":300},"id":"XeGsHYTt8IXU","outputId":"21292320-b891-4233-968f-33d8e51e67e1"},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1600x900 with 2 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os import linesep\n","from mpmath import sin,cos,tan,csc,sec,cot\n","from fractions import Fraction\n","import numpy as np\n","import matplotlib.pyplot as plt\n","from matplotlib import animation,rc\n","rc('animation', html='jshtml')\n","plt.rcParams.update({\"font.family\" : \"sans serif\",\"mathtext.fontset\" : \"cm\"})\n","\n","#parameters\n","clst=['lightskyblue','violet','aqua','cornflowerblue','yellow','w',(.1,.1,.1)] #colors dark bg\n","# clst=['mediumblue','violet','c','r','navy','k','w'] #colors light bg\n","Nf = 1440\n","# Nf=36\n","Nd = 16 # number of decimals\n","div = np.linspace(0,(1-1/Nf),Nf) #total divs\n","theta_deg=div*360\n","theta_rad=div*2*np.pi\n","ejth = np.exp(1j*theta_rad)\n","\n","#set up figures\n","fig = plt.figure(figsize=(16,9),facecolor=clst[-1])\n","fig.tight_layout()\n","ax_frame = [[[0, 1/18, .5, 8/9], [-1.3,1.3], [-1.3,1.3]], #complex plane\n"," [[.5, 0, .5, 1], [0,1], [0,1]], #numericals\n"," ]# [pos-boundary, xlim, ylim] for subplots 9:9\n","ax_lst=[] #axis list or the list of subplots\n","txt_lst=[] #list of y texts\n","line_lst = [] #array containing all the line segments\n","for k in range(len(ax_frame)):\n"," xn,xm,yn,ym = ax_frame[k][1]+ax_frame[k][2]\n"," ax=fig.add_axes(ax_frame[k][0],xlim=[xn,xm], ylim=[yn,ym],fc='none') #no fc\n"," ax.axis('off') #turn off axis frames\n"," ax_lst.append(ax)\n"," if k==0:\n"," ax.annotate(\"\", (xm, 0), (xn, 0),arrowprops={'arrowstyle':\"->\",'color':clst[-2]}) #x-axis\n"," ax.annotate(\"\", (0,ym), (0,yn),arrowprops={'arrowstyle':\"->\",'color':clst[-2]}) #y-axis\n"," ax.text(0.01,ym,'$Im$',color=clst[-2],size=20,va='center') #y label\n"," ax.text(xm-.02,0,'$Re$',size=20,va='top',ha='right',color=clst[-2]) #x-axis label\n"," line_lst.append(ax.plot([],[],color=clst[1],lw=3)[0]) #arc\n"," line_lst.append(ax.plot([],[],color=clst[0],lw=3)[0]) #run\n"," line_lst.append(ax.plot([],[],color=clst[2],lw=3)[0]) #rise\n"," line_lst.append(ax.plot([],[],color=clst[4],lw=3)[0]) #hyp\n"," line_lst.append(ax.plot([],[],color=clst[1],lw=1)[0]) #theta angle arc\n"," line_lst.append(ax.plot([],[],color=clst[4],ls='',marker='o',markersize=15)[0]) #dot\n","\n"," txt_theta = ax.text(.25,0,r'$\\theta$',size=28,color=clst[1])\n"," txt_ejt = ax.text(1,0,r'$e^{j\\theta}$',size=36,color=clst[4])\n"," txt_sin = ax.text(1,0,r'$\\sin\\theta$',size=28,color=clst[2],va='center')\n"," txt_cos = ax.text(.5,0,r'$\\cos\\theta$',size=28,color=clst[0],ha='center')\n"," if k==1:\n"," for mm in range(2):\n"," for m in range(4):\n"," if mm==0 and m==0:\n"," txt_lst.append(ax.text(0,.8-m*.2,'',size=24,color=clst[1]))\n"," elif mm==1 and m==0:\n"," txt_lst.append(ax.text(.4,.8-m*.2,'',size=21,color=clst[4]))\n"," elif mm==0 and m==1:\n"," txt_lst.append(ax.text(mm*.475,.8-m*.2,'',size=19,color=clst[2])) #sin\n"," elif mm==0 and m==2:\n"," txt_lst.append(ax.text(mm*.475,.8-m*.2,'',size=19,color=clst[0])) #cos\n"," else:\n"," txt_lst.append(ax.text(mm*.475,.8-m*.2,'',size=19,color=clst[-2]))\n","ax_lst[0].plot(ejth.real,ejth.imag,color=clst[0],lw=1,alpha=0.2)\n","\n","# animation function. This is called sequentially\n","def animate(i):\n"," # i=3\n"," line_lst[0].set_data(ejth[:i+1].real,ejth[:i+1].imag)\n"," line_lst[1].set_data([0,ejth[i].real],[0,0])\n"," line_lst[2].set_data([ejth[i].real,ejth[i].real],[0,ejth[i].imag])\n"," line_lst[3].set_data([0,ejth[i].real],[0,ejth[i].imag])\n"," line_lst[4].set_data(.25*ejth[:i+1].real,.25*ejth[:i+1].imag)\n"," line_lst[5].set_data([ejth[i].real],[ejth[i].imag])\n"," txt_ejt.set_position((cos(theta_rad[i]),sin(theta_rad[i])))\n"," if cos(theta_rad[i])>0:\n"," txt_ejt.set_ha('left')\n"," txt_sin.set_ha('left')\n"," else:\n"," txt_ejt.set_ha('right')\n"," txt_sin.set_ha('right')\n","\n"," if sin(theta_rad[i])>0:\n"," txt_ejt.set_va('bottom')\n"," txt_cos.set_va('top')\n"," else:\n"," txt_ejt.set_va('top')\n"," txt_cos.set_va('bottom')\n"," if cos(.5*theta_rad[i])>0:\n"," txt_theta.set_ha('left')\n"," else:\n"," txt_theta.set_ha('right')\n","\n","\n"," txt_theta.set_position((.25*cos(.5*theta_rad[i]),.25*sin(.5*theta_rad[i])))\n"," txt_cos.set_position((.5*cos(theta_rad[i]),0))\n"," txt_sin.set_position((cos(theta_rad[i]),.5*sin(theta_rad[i])))\n","\n"," txt_lst[0].set_text(r'$\\theta='+str(round(theta_deg[i],4))+\n"," r'^\\circ=\\frac{'+str(Fraction(i,Nf).numerator)+'}{'\n"," +str(Fraction(i,Nf).denominator)+'}\\pi$')\n"," txt_lst[2].set_text(r'$\\cos\\theta ='+str(round(cos(theta_rad[i]),Nd))+'$')\n"," txt_lst[1].set_text(r'$\\sin\\theta ='+str(round(sin(theta_rad[i]),Nd))+'$')\n"," if cos(theta_rad[i])==0:\n"," txt_lst[3].set_text(r'$\\tan\\theta =\\infty$')\n"," txt_lst[6].set_text(r'$\\sec\\theta =\\infty$')\n"," else:\n"," txt_lst[3].set_text(r'$\\tan\\theta ='+str(round(tan(theta_rad[i]),Nd))+'$')\n"," txt_lst[6].set_text(r'$\\sec\\theta ='+str(round(sec(theta_rad[i]),Nd))+'$')\n","\n"," if sin(theta_rad[i])<0:\n"," txt_lst[4].set_text(r'$e^{j\\theta} ='+str(round(cos(theta_rad[i]),int(.5*Nd)))+'-j'+\n"," str(round(-sin(theta_rad[i]),int(.5*Nd)))+'$')\n"," else:\n"," txt_lst[4].set_text(r'$e^{j\\theta} ='+str(round(cos(theta_rad[i]),int(.5*Nd)))+'+j'+\n"," str(round(sin(theta_rad[i]),int(.5*Nd)))+'$')\n"," if sin(theta_rad[i])==0:\n"," txt_lst[5].set_text(r'$\\csc\\theta =\\infty$')\n"," txt_lst[7].set_text(r'$\\cot\\theta =\\infty$')\n"," else:\n"," txt_lst[5].set_text(r'$\\csc\\theta ='+str(round(csc(theta_rad[i]),Nd))+'$')\n"," txt_lst[7].set_text(r'$\\cot\\theta ='+str(round(cot(theta_rad[i]),Nd))+'$')\n"," return\n","\n","anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=200)\n","# anim #uncomment to generate animation in the output area\n","# to save the animation, uncomment the following three lines\n","fn = \"TrigNum.mp4\"\n","writervideo = animation.FFMpegWriter(fps=1)\n","anim.save(fn, writer=writervideo,dpi = 120)"]}],"metadata":{"colab":{"provenance":[{"file_id":"1cjVqodYXle9-tR8gFWaiDVDq73vuxSR6","timestamp":1602944994194}]},"kernelspec":{"display_name":"Python 3","name":"python3"}},"nbformat":4,"nbformat_minor":0}