{
"query": {
"display": "$$\\tan\\left(θ\\right)=-\\frac{5}{4}$$",
"symbolab_question": "EQUATION#\\tan(θ)=-\\frac{5}{4}"
},
"solution": {
"level": "PERFORMED",
"subject": "Trigonometry",
"topic": "Trig Equations",
"subTopic": "Trig Equations",
"default": "θ=-0.89605…+πn",
"degrees": "θ=-51.34019…^{\\circ }+180^{\\circ }n",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\tan\\left(θ\\right)=-\\frac{5}{4}{\\quad:\\quad}θ=-0.89605…+πn$$",
"input": "\\tan\\left(θ\\right)=-\\frac{5}{4}",
"steps": [
{
"type": "interim",
"title": "Apply trig inverse properties",
"input": "\\tan\\left(θ\\right)=-\\frac{5}{4}",
"result": "θ=\\arctan\\left(-\\frac{5}{4}\\right)+πn",
"steps": [
{
"type": "step",
"primary": "General solutions for $$\\tan\\left(θ\\right)=-\\frac{5}{4}$$",
"secondary": [
"$$\\tan\\left(x\\right)=-a\\quad\\Rightarrow\\quad\\:x=\\arctan\\left(-a\\right)+πn$$"
],
"result": "θ=\\arctan\\left(-\\frac{5}{4}\\right)+πn"
}
],
"meta": {
"interimType": "Trig Apply Inverse Props 0Eq"
}
},
{
"type": "step",
"primary": "Show solutions in decimal form",
"result": "θ=-0.89605…+πn"
}
],
"meta": {
"solvingClass": "Trig Equations",
"practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations",
"practiceTopic": "Trig Equations"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "θ",
"plotRequest": "\\tan(θ)+\\frac{5}{4}"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
Solution
+1
Degrees
Solution steps
Apply trig inverse properties
General solutions for
Show solutions in decimal form
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Popular Examples
Frequently Asked Questions (FAQ)
What is the general solution for tan(θ)=-5/4 ?
The general solution for tan(θ)=-5/4 is θ=-0.89605…+pin