Poll Results
No votes. Be the first one to vote.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
To find the spherical coordinates ((rho, theta, phi)) of the Cartesian point (A(2, 3, -1)), we can use the following formulas:
1. (rho = sqrt{x^2 + y^2 + z^2})
2. (theta = tan^{-1}left(frac{y}{x}right))
3. (phi = cos^{-1}left(frac{z}{rho}right))
Given (x = 2), (y = 3), and (z = -1):
1. Calculate (rho):
[
rho = sqrt{2^2 + 3^2 + (-1)^2} = sqrt{4 + 9 + 1} = sqrt{14}
]
2. Calculate (theta):
[
theta = tan^{-1}left(frac{3}{2}right) approx 0.9828 , text{radians} quad (text{or } 56.31^circ)
]
3. Calculate (phi):
[
phi = cos^{-1}left(frac{-1}{sqrt{14}}right) approx cos^{-1}(-0.2673) approx 1.839 , text
Answer: b
Explanation: r = √(x2+y2+z2
) = √14 = 3.74
Θ = cos-1
(z/r) = cos-1
(-1/3.74) = 105.5⁰
Φ = tan-1
(y/x) = tan-1
(3/2) = 56.31⁰.
Answer: b
Explanation: r = √(x2+y2+z2) = √14 = 3.74
Θ = cos-1(z/r) = cos-1(-1/3.74) = 105.5⁰
Φ = tan-1(y/x) = tan-1(3/2) = 56.31⁰.