Find the Cartesian coordinates of B(4,25⁰,120⁰)

To convert spherical coordinates ( B(r, theta, phi) = B(4, 25^circ, 120^circ) ) into Cartesian coordinates ( (x, y, z) ), we use the following formulas:

1. ( x = r cdot sin(theta) cdot cos(phi) )
2. ( y = r cdot sin(theta) cdot sin(phi) )
3. ( z = r cdot cos(theta) )

Where:

– ( r ) is the radius,

– ( theta ) is the polar angle (measured from the positive z-axis),

– ( phi ) is the azimuthal angle (measured from the positive x-axis in the x-y plane).

Given:

– ( r = 4 )

– ( theta = 25^circ )

– ( phi = 120^circ )

First, convert angles from degrees to radians:

– ( theta = 25^circ = frac{25 pi}{180} approx 0.436 , text{radians} )

– ( phi = 120^circ = frac{120 pi}{180} = frac{2pi}{3} approx 2.094 , text{radians} )

Now, calculate the Cartesian coordinates:

1.