Question

Change from rectangular to spherical coordinates. (let ≥ 0, 0 ≤ ≤ 2, and 0 ≤ ≤. ) (a) (5, 5 3 , 10 3 )

Answer 1

The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Here, the given rectangular coordinate is (5, 5.3, 10.3).

Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.

We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.

We know, ρ² = (x²+y²+z²)

Therefore, ρ

= √(x²+y²+z²)

= √[(5)²+(5.3)²+(10.3)²]

= √(25+28.09+106.09)

= √(159.18)

= 12.62

Again, tan θ = (y/x)

Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°

Similarly, cos Φ = (z/ρ)

Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°

Here, the spherical coordinate is (ρ, θ, Φ).

Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).

Learn more about the conversion of a rectangular coordinate to a spherical coordinate here: brainly.com/question/17185505

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