{
"query": {
"display": "cartesian to polar $$\\left(3,\\:4\\right)$$",
"symbolab_question": "POLAR#polar (3,4)"
},
"solution": {
"level": "PERFORMED",
"subject": "Pre Calculus",
"topic": "Polar Coordinates",
"subTopic": "Polar",
"default": "(5,\\arctan(\\frac{4}{3}))"
},
"steps": {
"type": "interim",
"title": "Convert $$\\left(3,\\:4\\right)\\:$$to polar coordinates:$${\\quad}\\left(5,\\:\\arctan\\left(\\frac{4}{3}\\right)\\right)$$",
"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": [
"$$x=3$$",
"$$y=4$$"
]
},
{
"type": "step",
"primary": "$$r=\\sqrt{x^2+y^2}$$",
"result": "r=\\sqrt{3^{2}+4^{2}}"
},
{
"type": "interim",
"title": "$$\\sqrt{3^{2}+4^{2}}=5$$",
"input": "\\sqrt{3^{2}+4^{2}}",
"steps": [
{
"type": "step",
"primary": "$$3^{2}=9$$",
"result": "=\\sqrt{9+4^{2}}"
},
{
"type": "step",
"primary": "$$4^{2}=16$$",
"result": "=\\sqrt{9+16}"
},
{
"type": "step",
"primary": "Add the numbers: $$9+16=25$$",
"result": "=\\sqrt{25}"
},
{
"type": "step",
"primary": "Factor the number: $$25=5^{2}$$",
"result": "=\\sqrt{5^{2}}"
},
{
"type": "step",
"primary": "Apply radical rule: $$\\sqrt[n]{a^n}=a$$",
"secondary": [
"$$\\sqrt{5^{2}}=5$$"
],
"result": "=5",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7UouBdNlrW6tL1U+OaLJtCl1iJRJdZU8Snq+IOvMxYQFwkKGJWEPFPk38sdJMsyPIq747sIktGp6hsgp+0MGIfQtUCuEfAr4YiOd9j13RZoTx4Xi3iEiXperGhgn+F5Hb"
}
},
{
"type": "step",
"result": "r=5"
},
{
"type": "step",
"primary": "$$\\theta=\\arctan\\left(\\frac{y}{x}\\right)$$",
"result": "θ=\\arctan\\left(\\frac{4}{3}\\right)"
},
{
"type": "step",
"primary": "The polar coordinates of $$\\left(3,\\:4\\right)$$",
"result": "\\left(5,\\:\\arctan\\left(\\frac{4}{3}\\right)\\right)"
}
]
}
}
Solution
cartesian to polar
Solution
Solution steps
The polar coordinates of