{
"query": {
"display": "solve for $$θ,\\:\\cot\\left(θ\\right)=-\\frac{π}{6}$$",
"symbolab_question": "SOLVE_FOR#solvefor θ,\\cot(θ)=-\\frac{π}{6}"
},
"solution": {
"level": "PERFORMED",
"subject": "Trigonometry",
"topic": "Trig Equations",
"subTopic": "Trig Equations",
"default": "θ=2.05314…+πn",
"degrees": "θ=117.63649…^{\\circ }+180^{\\circ }n",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$solve\\:for\\:θ,\\:\\cot\\left(θ\\right)=-\\frac{π}{6}{\\quad:\\quad}θ=2.05314…+πn$$",
"input": "\\cot\\left(θ\\right)=-\\frac{π}{6}",
"steps": [
{
"type": "interim",
"title": "Apply trig inverse properties",
"input": "\\cot\\left(θ\\right)=-\\frac{π}{6}",
"result": "θ=\\arccot\\left(-\\frac{π}{6}\\right)+πn",
"steps": [
{
"type": "step",
"primary": "General solutions for $$\\cot\\left(θ\\right)=-\\frac{π}{6}$$",
"secondary": [
"$$\\cot\\left(x\\right)=-a\\quad\\Rightarrow\\quad\\:x=\\arccot\\left(-a\\right)+πn$$"
],
"result": "θ=\\arccot\\left(-\\frac{π}{6}\\right)+πn"
}
],
"meta": {
"interimType": "Trig Apply Inverse Props 0Eq"
}
},
{
"type": "step",
"primary": "Show solutions in decimal form",
"result": "θ=2.05314…+πn"
}
],
"meta": {
"solvingClass": "Trig Equations",
"practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations",
"practiceTopic": "Trig Equations"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "θ",
"plotRequest": "\\cot(θ)+\\frac{π}{6}"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
solve for
Solution
+1
Degrees
Solution steps
Apply trig inverse properties
General solutions for
Show solutions in decimal form
Graph
Popular Examples
Frequently Asked Questions (FAQ)
What is the general solution for solvefor θ,cot(θ)=-pi/6 ?
The general solution for solvefor θ,cot(θ)=-pi/6 is θ=2.05314…+pin