{
"query": {
"display": "desplazamiento $$4\\sin\\left(3θ-\\frac{1}{3}π\\right)+1$$",
"symbolab_question": "FUNCTION#shift 4\\sin(3θ-\\frac{1}{3}π)+1"
},
"solution": {
"level": "PERFORMED",
"subject": "Functions & Graphing",
"topic": "Functions",
"subTopic": "shift",
"default": "\\mathrm{Fase}:\\frac{π}{9},\\:\\mathrm{Vertical}:1",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Desplazamiento de $$4\\sin\\left(3θ-\\frac{1}{3}π\\right)+1:{\\quad}$$Fase$$:\\frac{π}{9},\\:\\:$$Vertical$$:1$$",
"steps": [
{
"type": "definition",
"title": "Definición de desplazamiento",
"text": "Para $$f\\left(x\\right)=A{\\cdot}g\\left(Bx-C\\right)+D$$, donde $$g\\left(x\\right)$$ es una de las funciones trigonométricas básicas, <br/>$$\\frac{C}{B}$$ es llamado desplazamiento de fase <br/>$$D$$ es llamado desplazamiento vertical"
},
{
"type": "interim",
"title": "Simplificar $$4\\sin\\left(3θ-\\frac{1}{3}π\\right)+1:{\\quad}4\\sin\\left(3θ-\\frac{π}{3}\\right)+1$$",
"input": "4\\sin\\left(3θ-\\frac{1}{3}π\\right)+1",
"steps": [
{
"type": "interim",
"title": "$$\\frac{1}{3}π=\\frac{π}{3}$$",
"input": "\\frac{1}{3}π",
"steps": [
{
"type": "step",
"primary": "Multiplicar fracciones: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$",
"result": "=\\frac{1π}{3}"
},
{
"type": "step",
"primary": "Multiplicar: $$1π=π$$",
"result": "=\\frac{π}{3}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s772I7EUUf95BSZLtUnBRqOACWKUbvV6WK3fDUgFtg3Q/ysS6ztOAKKFAEXmiY4WQmAonq/n3jQ0ddQ1SaaPv11c1bIZxfodm3UsZcfZAZr4vkhcFupvBZeQVoyGlC+ZKTuNtnTCAhUVHtS+6YazBAQQ=="
}
},
{
"type": "step",
"result": "=4\\sin\\left(3θ-\\frac{π}{3}\\right)+1"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s76cV9vr+rRKMYwsvGWq+AKkWjrDkBItR8MRDcZM/LONVV00rpv8+ZC6TM10tVCSHslFSVkxrxkAklcCEjrnolWf3r1JJoufY0TjRXsw2kvZMj2HLr5XkgDz1O/djA+zZzHjb2+5NLFZrsH9fcPWg/TVQPtlzqbBh0TlBdm4jArY/nOw8N/cJIckNaE7xG3gfUhFiaXq8QusrXGvHi6b87jw=="
}
},
{
"type": "step",
"primary": "$$f\\left(x\\right)=4\\sin\\left(3θ-\\frac{π}{3}\\right)+1$$<br/>$$g\\left(Bx-C\\right)=\\sin\\left(3θ-\\frac{π}{3}\\right),\\:B=3,\\:C=\\frac{π}{3},\\:D=1$$<br/>Por lo tanto, el desplazamiento de fase $$\\frac{C}{B}$$ es $$\\frac{\\frac{π}{3}}{3}$$",
"result": "\\frac{π}{9}"
},
{
"type": "step",
"primary": "El desplazamiento vertical $$D$$ es $$1$$",
"result": "1"
}
],
"meta": {
"solvingClass": "Function Shift"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "θ",
"plotRequest": "4\\sin(3θ-\\frac{π}{3})+1"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solución
desplazamiento
Solución
Pasos de solución
Simplificar
Por lo tanto, el desplazamiento de fase es
El desplazamiento vertical es