{
"query": {
"display": "cartesian to polar $$\\left(2,\\:3\\right)$$",
"symbolab_question": "POLAR#polar (2,3)"
},
"solution": {
"level": "PERFORMED",
"subject": "Pre Calculus",
"topic": "Polar Coordinates",
"subTopic": "Polar",
"default": "(\\sqrt{13},\\arctan(\\frac{3}{2}))"
},
"steps": {
"type": "interim",
"title": "Convert $$\\left(2,\\:3\\right)\\:$$to polar coordinates:$${\\quad}\\left(\\sqrt{13},\\:\\arctan\\left(\\frac{3}{2}\\right)\\right)$$",
"steps": [
{
"type": "definition",
"title": "Definition",
"text": "To convert Cartesian coordinates $$\\left(x,\\:y\\right)\\:$$to Polar coordinates $$\\left(r,\\:\\theta\\right)\\:$$apply:<br/>$$r=\\sqrt{x^2+y^2}\\quad\\theta=\\arctan\\left(\\frac{y}{x}\\right)$$",
"secondary": [
"$$x=2$$",
"$$y=3$$"
]
},
{
"type": "step",
"primary": "$$r=\\sqrt{x^2+y^2}$$",
"result": "r=\\sqrt{2^{2}+3^{2}}"
},
{
"type": "step",
"primary": "Simplify",
"result": "r=\\sqrt{13}"
},
{
"type": "step",
"primary": "$$\\theta=\\arctan\\left(\\frac{y}{x}\\right)$$",
"result": "θ=\\arctan\\left(\\frac{3}{2}\\right)"
},
{
"type": "step",
"primary": "The polar coordinates of $$\\left(2,\\:3\\right)$$",
"result": "\\left(\\sqrt{13},\\:\\arctan\\left(\\frac{3}{2}\\right)\\right)"
}
]
}
}
Solution
cartesian to polar
Solution
Solution steps
Simplify
The polar coordinates of