Convert $( 1,1 , \sqrt { 2 } )$ From Rectangular Coordinates to Spherical Coordinates

question 5

Multiple Choice

Convert $( 1,1 , \sqrt { 2 } )$ from rectangular coordinates to spherical coordinates.

• A) \(\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)\)
• B) \(\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 4 } \right)\)
• C) \(\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)\)
• D) \(\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 4 } \right)\)
• E) \(\left( \sqrt { 2 } , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)\)
• F) \(\left( 2 , \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)\)
• G) \(\left( \sqrt { 2 } , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)\)
• H) \(\left( 2 , \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)\)

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Definitions:

Quantifier

In logic, an expression (such as "all", "some", or "no") that indicates the quantity of specimens to which a proposition applies.

Atomic Open Sentence

A sentence in formal logic that contains a variable and becomes a proposition when the variable is replaced by a definite term.

Truth-functional

Pertaining to a logical or linguistic expression whose truth or falsehood depends only on the truth or falsehood of its components.

Atomic

Pertaining to atoms, the smallest units of matter that retain the properties of an element.