The Point (6, Pi/3, Pi/4) Is Given In Spherical Coordinates. Plot The Point And Find Its Rectangular Coordinates. We Plot The Point In The Figure. From The Equations To Convert Spherical To Rectangular Coordinates We Have X = Rho Sin(Phi)Cos(Theta) = 6sin(Pi/4)Cos(Pi/3) = 6(1/2 Middoot Squareroot 3)(1/2) = 3/2 Middot Squareroot 2 Y = Rho

 

 

 

EXAMPLE 1 The point (6, x/3, x/4) is given in spherical coordinates. Plot the point and find its rectangular coordinates. SOLUTION We plot the point in the figure. From the equations to convert spherical to rectangular coordinates we have x=psin(p)cos(0) = 6sin(x/4)cos(x/3) Video Example Tutorial Online Textbook 2 .2 xx() y psin(p)sin(e) 6sin(x/4)sin(/3) 2 63 xx .)- 6 - z=pcos(p)=6cos(1/4) -60 12 Thus the point (6, /3, /4) is ( x 3 6 2 x. 6 2 2 X) in rectangular coordinates.