{
"query": {
"display": "$$\\tan\\left(a\\right)=\\sqrt{\\frac{15}{7}},\\:\\sin\\left(a\\right)$$",
"symbolab_question": "EQUATION#\\tan(a)=\\sqrt{\\frac{15}{7}},\\sin(a)"
},
"solution": {
"level": "PERFORMED",
"subject": "Trigonometry",
"topic": "Trig Equations",
"subTopic": "Trig Equations",
"default": "\\mathrm{No\\:Solution\\:for}\\:a\\in\\mathbb{R}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\tan\\left(a\\right)=\\sqrt{\\frac{15}{7}},\\:\\sin\\left(a\\right){\\quad:\\quad}$$No Solution for $$a\\in\\mathbb{R}$$",
"input": "\\tan\\left(a\\right)=\\sqrt{\\frac{15}{7}},\\:\\sin\\left(a\\right)",
"steps": [
{
"type": "interim",
"title": "Apply trig inverse properties",
"input": "\\tan\\left(a\\right)=\\sqrt{\\frac{15}{7}}",
"result": "a=\\arctan\\left(\\sqrt{\\frac{15}{7}}\\right)+πn",
"steps": [
{
"type": "step",
"primary": "General solutions for $$\\tan\\left(a\\right)=\\sqrt{\\frac{15}{7}}$$",
"secondary": [
"$$\\tan\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arctan\\left(a\\right)+πn$$"
],
"result": "a=\\arctan\\left(\\sqrt{\\frac{15}{7}}\\right)+πn"
}
],
"meta": {
"interimType": "Trig Apply Inverse Props 0Eq"
}
},
{
"type": "step",
"primary": "Solutions for the range $$\\sin\\left(a\\right)$$",
"result": "\\mathrm{No\\:Solution\\:for}\\:a\\in\\mathbb{R}"
}
],
"meta": {
"solvingClass": "Trig Equations",
"practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations",
"practiceTopic": "Trig Equations"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "a",
"plotRequest": "\\tan(a)-\\sqrt{\\frac{15}{7}},\\sin(a)"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
Solution
Solution steps
Apply trig inverse properties
General solutions for
Solutions for the range
Graph
Popular Examples
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Frequently Asked Questions (FAQ)
What is the general solution for tan(a)=sqrt(15/7),sin(a) ?
The general solution for tan(a)=sqrt(15/7),sin(a) is No Solution for a\in\mathbb{R}