Off[General::spell]
Off[General::spell1]

Cartesian Coordinate System

x  =  0.64;
y  = 0.5;
z  =  0.5;

    
<< Graphics`Graphics3D`

Circular Coordinate System

Rs  =  (x^2) + (y^2) + (z^2);
θs  =  
        ArcTan[((x^2) + (y^2))/z];
ϕs  =  ArcTan[y/x];

    
spherer   =  
        ParametricPlot3D[{Rs Sin[θ] Cos[ϕ], 
            Rs Sin[θ] Sin[ϕ],  Rs Cos[θ], 
            EdgeForm[]}, {θ, 0, π}, {ϕ, 1.2  π/4, 
            7  π/4}, 
          DisplayFunction -> Identity];

    
rsinthcircle =  
        ParametricPlot3D[{Rs Sin[θs] Cos[ϕ], 
            Rs Sin[θs] Sin[ϕ],  Rs Cos[θs]}, {ϕ, 
            0, 2  π}, 
          DisplayFunction -> Identity];

    
projedge1  = 
        Graphics3D[{Dashing[{0.010, 0.010}], 
            Line[{{0, 0, 0}, {Rs Sin[θs] Cos[ϕs], 
                  Rs Sin[θs] Sin[ϕs],  
                  Rs Cos[θs]}}]}]; 
xyprojedge1z  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{0, 0, 
                Rs Cos[θs]}, {Rs Sin[θs] Cos[ϕs], 
                Rs Sin[θs] Sin[ϕs],  
                Rs Cos[θs]}}]}];  
    xyprojedge1  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{0, 0, 0}, {Rs Sin[θs] Cos[ϕs], 
                Rs Sin[θs] Sin[ϕs],  0}}]}];  
    dropxyprojedge1  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{Rs Sin[θs] Cos[ϕs], 
                Rs Sin[θs] Sin[ϕs],  
                0}, {Rs Sin[θs] Cos[ϕs], 
                Rs Sin[θs] Sin[ϕs],  
                Rs Cos[θs]}}]}]; 
xprojedge1  = 
        Graphics3D[{Dashing[{0.010, 0.010}], 
            Line[{{Rs Sin[θs] Cos[ϕs], 0,  
                  0}, {Rs Sin[θs] Cos[ϕs], 
                  Rs Sin[θs] Sin[ϕs],  
                  0}}]}]; 
yprojedge1  = 
        Graphics3D[{Dashing[{0.010, 0.010}], 
            Line[{{0, Rs Sin[θs] Sin[ϕs],  
                  0}, {Rs Sin[θs] Cos[ϕs], 
                  Rs Sin[θs] Sin[ϕs],  
                  0}}]}]; 

rsinthline  =  
        Graphics3D[
          Line[{{0, 0, 
                Rs Cos[θs]}, {Rs Sin[θs] Cos[ϕs], 
                Rs Sin[θs] Sin[ϕs],  
                Rs Cos[θs]}}]];

    
tharc  =  
        ParametricPlot3D[{0.45 Rs Sin[θ] Cos[ϕs], 
            0.45  Rs Sin[θ] Sin[ϕs],  
            0.45 Rs Cos[θ]}, {θ, 0, θs}, 
          DisplayFunction -> Identity];
pharc  =  
        ParametricPlot3D[{0.45  Rs Sin[θs] Cos[ϕ], 
            0.45  Rs Sin[θs] Sin[ϕ],  0}, {ϕ, 
            0, ϕs}, 
          DisplayFunction -> 
            Identity];


radiallines  =  projedge1;
projectedlines  =  {xyprojedge1z, xyprojedge1, dropxyprojedge1, 
          xprojedge1, yprojedge1};
long  =  Rs;
xa  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {long, 0, 0}}],  
            Text["x", {long + 0.05, 0, 
                0}]}];
ya  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, long, 0}}],  
            Text["y", {0.0, 
                long + 0.05, -0.0}]}];
za  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, 0, long}}],  
            Text["z", {0.0, -0.0, 
                long + 0.05}]}];
axessetup  =  {xa, ya, za};
lab1  =  
        Graphics3D[
          Text[ "R Sin θ", {6/8  
                Rs Sin[θs/2] Cos[ϕs], 
              6/8  Rs Sin[θs/2] Sin[ϕs], 
              7/9  Rs Cos[θs/2]}]];
lab2  =  
        Graphics3D[
          Text[ "R", {3  Rs/5 Sin[9  θs/8] Cos[ϕs], 
              3  Rs/5 Sin[9  θs/8] Sin[ϕs],  
              3  Rs/5 Cos[9  θs/8]}]];
lab3  =  
        Graphics3D[
          Text[ "θ", {Rs/2 Sin[θs/2] Cos[ϕs], 
              Rs/2 Sin[θs/2] Sin[ϕs],  
              Rs/2 Cos[θs/2]}]];
lab4  =  
        Graphics3D[
          Text[ "ϕ", {0.46 Sin[π/2] Cos[ϕs/2], 
              0.31 Sin[π/2] Sin[ϕs/2],  
              0}]];
lab5  =  
        Graphics3D[
          Text[ "R Cos θ", {8/8  
                Rs Sin[3  θs/2] Cos[ϕs], 
              7/8  Rs Sin[3  θs/2] Sin[ϕs],  
              12/8  Rs Cos[3  θs/2]}]];
lab6  =  
        Graphics3D[
          Text[ "R Sin θ Sin ϕ", {7/8  Rs , Rs/6, 
              0}]];
lab7  =  
        Graphics3D[
          Text[ "R Sin θ Cos ϕ", {4/8  Rs , -Rs/6, 
              0}]];

    
labels2  =  {lab1, lab2, lab3, lab4, lab5, lab6, 
          lab7};
p2  =  
        Show[{tharc, pharc, projedge1, projectedlines, axessetup, 
            labels2
}, PlotRange -> All, 
          Boxed -> False, Axes -> False, 
          ViewCenter -> {1/2, 1/2, 1/2}, ViewPoint -> {8, -5, 1.75}, 
          DisplayFunction -> Identity];
long = 1.075;
xa  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {long, 0, 0}}],  
            Text["x", {long + 0.15, 0, 
                0}]}];
ya  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, long, 0}}],  
            Text["y", {0.0, 
                long + 0.15, -0.0}]}];
za  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, 0, long}}],  
            Text["z", {0.0, -0.0, 
                long + 0.15}]}];
axessetup  =  {xa, ya, za};
p4  =  
        Show[{rsinthcircle, spherer, axessetup, radiallines, projectedlines}, 
          PlotRange -> All, Axes -> False, Boxed -> False, 
          ViewPoint -> {2.5, 1.15, 1.15}, SphericalRegion -> True, 
          LightSources -> {{{-10, -5, 10}, 
                RGBColor[1, 1, 0]}, {{1, 5,  .1}, 
                RGBColor[0, 1, 1]}, {{-15, -10, -10}, 
                RGBColor[0, 1, 1]}}]; 
  
Show[GraphicsArray[{p4, p2}]
, 
        DisplayFunction -> $DisplayFunction];

Cylindrical Coordinate System

rc  =  (x^2) + (y^2);
ϕc  =  ArcTan[y/x];
zc  =  z;

    
cylinderr   =  
        ParametricPlot3D[{rc Cos[ϕ], rc  Sin[ϕ],  z, 
            EdgeForm[]}, {z, -1, 1}, {ϕ, 1.2  π/4, 7  π/4}, 
          DisplayFunction -> Identity];

    
zcircle =  
        ParametricPlot3D[{rc Cos[ϕ], rc  Sin[ϕ],  zc}, {ϕ, 
            0, 2  π}, 
          DisplayFunction -> Identity];

    
xyprojedge1z  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{0, 0, zc}, {rc Cos[ϕc], rc  Sin[ϕc],  
                zc}}]}];  
    xyprojedge1  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{0, 0, 0}, {rc Cos[ϕc], rc  Sin[ϕc],  0}}]}];  
    dropxyprojedge1  = 
      Graphics3D[{Dashing[{0.010, 0.010}], 
          Line[{{rc Cos[ϕc], rc  Sin[ϕc],  
                zc}, {rc Cos[ϕc], rc  Sin[ϕc],  
                0}}]}]; 
xprojedge1  = 
        Graphics3D[{Dashing[{0.010, 0.010}], 
            Line[{{rc Cos[ϕc], 0,  0}, {rc  Cos[ϕc], 
                  rc Sin[ϕc],  0}}]}]; 
yprojedge1  = 
        Graphics3D[{Dashing[{0.010, 0.010}], 
            Line[{{0, rc Sin[ϕc],  0}, {rc Cos[ϕc], 
                  rc  Sin[ϕc],  
                  0}}]}]; 

pharc  =  
        ParametricPlot3D[{0.45  rc Sin[θs] Cos[ϕ], 
            0.45  rc Sin[θs] Sin[ϕ],  0}, {ϕ, 
            0, ϕc}, 
          DisplayFunction -> Identity];

    
projectedlines  =  {xyprojedge1z, xyprojedge1, dropxyprojedge1, 
          xprojedge1, yprojedge1};
long  =  rc;
xa  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {long, 0, 0}}],  
            Text["x", {long + 0.05, 0, 
                0}]}];
ya  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, long, 0}}],  
            Text["y", {0.0, 
                long + 0.05, -0.0}]}];
za  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, 0, long}}],  
            Text["z", {0.0, -0.0, 
                long + 0.05}]}];
axessetup  =  {xa, ya, za};
lab2  =  
        Graphics3D[
          Text[ "r", {3  rc/6 Cos[ϕc], 3  rc/6  Sin[ϕc],  
              19/18 zc}]];
lab4  =  
        Graphics3D[
          Text[ "ϕ", {0.31 Cos[ϕc/3], 
              0.31  Sin[ϕc/3],  0}]];
lab5  =  
        Graphics3D[
          Text[ "z", {19/18  rc  Cos[ϕc], 
              19/18  rc  Sin[ϕc],  
              2/4 zc}]];
lab6  =  
        Graphics3D[
          Text[ "r Sin ϕ", {8/8  rc , rc/5, 
              0}]];
lab7  =  
        Graphics3D[
          Text[ "r Cos ϕ", {5/8  rc , -rc/6, 
              0}]];

    
labels2  =  {lab2, lab4, lab5, lab6, 
          lab7};
p1  =  
        Show[{pharc, projectedlines, axessetup, labels2
}, 
          PlotRange -> All, Boxed -> False, Axes -> False, 
          ViewCenter -> {1/2, 1/2, 1/2}, ViewPoint -> {8, -5, 1.75}, 
          DisplayFunction -> Identity];
long = 1.075;
xa  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {long, 0, 0}}],  
            Text["x", {long + 0.5, 0, 0}]}];
ya  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, long, 0}}],  
            Text["y", {0.0, 
                long + 0.15, -0.0}]}];
za  =  
        Graphics3D[{AbsoluteThickness[2], Line[{{0, 0, 0}, {0, 0, long}}],  
            Text["z", {0.0, -0.0, 
                long + 0.15}]}];
axessetup  =  {xa, ya, za};
p3  =  
        Show[{cylinderr,  zcircle, axessetup, projectedlines}, 
          PlotRange -> All, Axes -> False, Boxed -> False, 
          ViewPoint -> {2.5, 1.15, 1.15}, 
          LightSources -> {{{-10, -5, 10}, 
                RGBColor[1, 1, 0]}, {{1, 5,  .1}, 
                RGBColor[0, 1, 1]}, {{-15, -10, -10}, 
                RGBColor[0, 1, 1]}}]; 
  
Show[GraphicsArray[{p3, p1}]
, 
        DisplayFunction -> $DisplayFunction];

Show[GraphicsArray[{{p4, p2}, {p3, p1}}], 
        DisplayFunction -> $DisplayFunction];