{ "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 } }