arctan((-sqrt(2))/(-sqrt(2)))

{ "query": { "display": "$$\\arctan\\left(\\frac{-\\sqrt{2}}{-\\sqrt{2}}\\right)$$", "symbolab_question": "TRIG_EVALUATE#\\arctan(\\frac{-\\sqrt{2}}{-\\sqrt{2}})" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\frac{π}{4}", "decimal": "45", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\arctan\\left(\\frac{-\\sqrt{2}}{-\\sqrt{2}}\\right)=\\frac{π}{4}$$", "input": "\\arctan\\left(\\frac{-\\sqrt{2}}{-\\sqrt{2}}\\right)", "steps": [ { "type": "interim", "title": "Use the following trivial identity:$${\\quad}\\arctan\\left(\\frac{-\\sqrt{2}}{-\\sqrt{2}}\\right)=\\frac{π}{4}$$", "input": "\\arctan\\left(\\frac{-\\sqrt{2}}{-\\sqrt{2}}\\right)", "steps": [ { "type": "step", "primary": "$$\\begin{array}{|c|c|c|}\\hline x&\\arctan(x)&\\arctan(x)\\\\\\hline 0&0&0^{\\circ}\\\\\\hline \\frac{\\sqrt{3}}{3}&\\frac{\\pi}{6}&30^{\\circ}\\\\\\hline 1&\\frac{\\pi}{4}&45^{\\circ}\\\\\\hline \\sqrt{3}&\\frac{\\pi}{3}&60^{\\circ}\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "=\\frac{π}{4}" } ], "meta": { "interimType": "Trig Trivial Angle Value Title 0Eq" } }, { "type": "step", "result": "=\\frac{π}{4}" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }