Question

PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical coordinates for this point. SOLUTION From the distance formula we have ρ = x2 + y2 + z2 = 0 + 75 + 25 = 10 Correct: Your answer is correct. and so these equations give the following. cos(φ) = z ρ = -1/2 Correct: Your answer is correct. φ = $$ Incorrect: Your answer is incorrect. cos(θ) = x ρ sin(φ) = θ = (Note that θ ≠ 3π 2 because y = 5 2 > 0.) Therefore spherical coordinates of the given point are (ρ, θ, φ) = PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical coordinates for this point. SOLUTION From the distance formula we have ρ = x2 + y2 + z2 = 0 + 75 + 25 = 10 Correct: Your answer is correct. and so these equations give the following. cos(φ) = z ρ = -1/2 Correct: Your answer is correct. φ = $$ Incorrect: Your answer is incorrect. cos(θ) = x ρ sin(φ) = θ = (Note that θ ≠ 3π 2 because y = 5 2 > 0.) Therefore spherical coordinates of the given point are (ρ, θ, φ) =

Answer 1

Le t , (x,3,2) be the carte sinn (yectangulan) co-ordinatesa point P,G, φ) be the spherital co-oYdinates σ4that paint, then , 2 Suaring ama adding ue get

01 こ

AlsoZ=pc03 , 2TT 3 21T

Dividinge ot by O 543 "Х Baicaluy, sines Basical the iven point in 2eTo , 67n Hence, the line jnning 0γ1gm ama wwe makes am ae direction ^xis kno ine m 2 -plame 2. And, θ the a~-911 between the Une joining (χ3,2)3(055,-5) and origin ande positive dlivectiom Hence, T 2 (e, o,q).(to,TI72 , ) Hence, 2