sin(x)+sin^2(x)+cos(x)+cos^2(x)=0

{ "query": { "display": "$$\\sin\\left(x\\right)+\\sin^{2}\\left(x\\right)+\\cos\\left(x\\right)+\\cos^{2}\\left(x\\right)=0$$", "symbolab_question": "EQUATION#\\sin(x)+\\sin^{2}(x)+\\cos(x)+\\cos^{2}(x)=0" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=2πn+π,x=2πn+\\frac{3π}{2}", "degrees": "x=180^{\\circ }+360^{\\circ }n,x=270^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(x\\right)+\\sin^{2}\\left(x\\right)+\\cos\\left(x\\right)+\\cos^{2}\\left(x\\right)=0{\\quad:\\quad}x=2πn+π,\\:x=2πn+\\frac{3π}{2}$$", "input": "\\sin\\left(x\\right)+\\sin^{2}\\left(x\\right)+\\cos\\left(x\\right)+\\cos^{2}\\left(x\\right)=0", "steps": [ { "type": "interim", "title": "Rewrite using trig identities", "input": "\\cos\\left(x\\right)+\\sin\\left(x\\right)+1", "result": "1+\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)=0", "steps": [ { "type": "interim", "title": "$$\\sin\\left(x\\right)+\\cos\\left(x\\right)=\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)$$", "input": "\\sin\\left(x\\right)+\\cos\\left(x\\right)", "steps": [ { "type": "step", "primary": "Rewrite as", "result": "=\\sqrt{2}\\left(\\frac{1}{\\sqrt{2}}\\sin\\left(x\\right)+\\frac{1}{\\sqrt{2}}\\cos\\left(x\\right)\\right)" }, { "type": "step", "primary": "Use the following trivial identity: $$\\cos\\left(\\frac{\\pi}{4}\\right)=\\frac{1}{\\sqrt{2}}$$", "secondary": [ "Use the following trivial identity: $$\\sin\\left(\\frac{\\pi}{4}\\right)=\\frac{1}{\\sqrt{2}}$$" ], "result": "=\\sqrt{2}\\left(\\cos\\left(\\frac{π}{4}\\right)\\sin\\left(x\\right)+\\sin\\left(\\frac{π}{4}\\right)\\cos\\left(x\\right)\\right)" }, { "type": "step", "primary": "Use the Angle Sum identity: $$\\sin\\left(s+t\\right)=\\sin\\left(s\\right)\\cos\\left(t\\right)+\\cos\\left(s\\right)\\sin\\left(t\\right)$$", "result": "=\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=1+\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)" } ], "meta": { "interimType": "Trig Rewrite Using Trig identities 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7lRPp6QndqgNT+L6IZutAbCMdtD7TRyyPHMsNO2w5AUIFMS0G0HgjUXwc3RQOmn9BYznLdIBaHD4ibBnEILJTDXUHW1mE5UQUTIwuQd6ag+xFcCVria0VBJjrvn819PR2Tu3FvYEB3AYuqlpPwaqiXeY5MMgkVbTN3pnCLEaGvFNFKk3fejFkyiOiq9iG9IkAO/B7UtNBfw19bDRpX2AlzDEZOhzOLFFCWOVe0TAs9Ps/tVtg7k21KzJIFYRgfW7H" } }, { "type": "interim", "title": "Move $$1\\:$$to the right side", "input": "1+\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)=0", "result": "\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)=-1", "steps": [ { "type": "step", "primary": "Subtract $$1$$ from both sides", "result": "1+\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)-1=0-1" }, { "type": "step", "primary": "Simplify", "result": "\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)=-1" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$\\sqrt{2}$$", "input": "\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)=-1", "result": "\\sin\\left(x+\\frac{π}{4}\\right)=-\\frac{\\sqrt{2}}{2}", "steps": [ { "type": "step", "primary": "Divide both sides by $$\\sqrt{2}$$", "result": "\\frac{\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)}{\\sqrt{2}}=\\frac{-1}{\\sqrt{2}}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)}{\\sqrt{2}}=\\frac{-1}{\\sqrt{2}}", "result": "\\sin\\left(x+\\frac{π}{4}\\right)=-\\frac{\\sqrt{2}}{2}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)}{\\sqrt{2}}:{\\quad}\\sin\\left(x+\\frac{π}{4}\\right)$$", "input": "\\frac{\\sqrt{2}\\sin\\left(x+\\frac{π}{4}\\right)}{\\sqrt{2}}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$\\sqrt{2}$$", "result": "=\\sin\\left(x+\\frac{π}{4}\\right)" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s74DwjiBDVBIb8+yh6fkkMMbn+mZOr6UCwUw6QoOQbUoqm8van+athsYxKAATCKgnHKRacX/xbFbNn3rfnX/fyYMzBWJotReR4P4m6RE6FZ2PLIjIvQqvagUmEBw4mPdGLjuMG+6OaNOXhG0cASZxRUE3kCh3oevUunZ7/b0qFKBSBAc1PafP4ia+acEW7bvr5wY8JT7ajsyOQBKfmpaSWOxLdr/IHB8VsUmrS1MXEJwbRUj4qvF1K7VD9344y9hND" } }, { "type": "interim", "title": "Simplify $$\\frac{-1}{\\sqrt{2}}:{\\quad}-\\frac{\\sqrt{2}}{2}$$", "input": "\\frac{-1}{\\sqrt{2}}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{b}=-\\frac{a}{b}$$", "result": "=-\\frac{1}{\\sqrt{2}}" }, { "type": "interim", "title": "Rationalize $$-\\frac{1}{\\sqrt{2}}:{\\quad}-\\frac{\\sqrt{2}}{2}$$", "input": "-\\frac{1}{\\sqrt{2}}", "result": "=-\\frac{\\sqrt{2}}{2}", "steps": [ { "type": "step", "primary": "Multiply by the conjugate $$\\frac{\\sqrt{2}}{\\sqrt{2}}$$", "result": "=-\\frac{1\\cdot\\:\\sqrt{2}}{\\sqrt{2}\\sqrt{2}}", "meta": { "title": { "extension": "To rationalize the denominator, multiply numerator and denominator by the conjugate of the radical $$\\sqrt{2}$$" } } }, { "type": "step", "primary": "$$1\\cdot\\:\\sqrt{2}=\\sqrt{2}$$" }, { "type": "interim", "title": "$$\\sqrt{2}\\sqrt{2}=2$$", "input": "\\sqrt{2}\\sqrt{2}", "result": "=-\\frac{\\sqrt{2}}{2}", "steps": [ { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a}\\sqrt{a}=a$$", "secondary": [ "$$\\sqrt{2}\\sqrt{2}=2$$" ], "result": "=2", "meta": { "practiceLink": "/practice/radicals-practice", "practiceTopic": "Radical Rules" } } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7OXRSLY4uXiMbvMfICP5T88aFSKFknkW7qg0U6E21MorMwViaLUXkeD+JukROhWdjBJz+17+I6kHbIEeqwhy4mdC5tTYOsrqRy+4iBsRgZTQLmgWGjI523GgzSlA2k6Cv" } } ], "meta": { "interimType": "Rationalize Title 1Eq" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7tkkS6M9CCT9LrMl7pDU/tr15eDTBjqr6Mh44dbONM5kJQJZuTAY5js+oqjdT8kslDa1hUvtzgBcwD7zey8pjX4xmKsrTmr07seOuQC7eif7WwPs1+Gw97t4MeuaNjSYTwPBBw3byB5RPtpSy6YLt2mmZmrN+TIHczZDNlT/7/mGJqVxX90jlMfh9fKn6dzC4" } }, { "type": "step", "result": "\\sin\\left(x+\\frac{π}{4}\\right)=-\\frac{\\sqrt{2}}{2}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ECl81GL+sHp+UX1O7owT7WbvTNJptQaSPijR+oJypm5S9NdbAQZUay2JfHZvlqXDHQdgN3VU4XCCh1zrrZ7JPZoyhYICkHY06PRn2J5cYsZ2mUx7UjX+gUWi9hUyGD/sPWyfTTHyVp4Zawjxo8WXIRLdr/IHB8VsUmrS1MXEJwbSv2RAooRJzVXVXhalul4403v9nA7hGUr+YKqgmYb1+g7upzez8Ly2EObkVpSZ9PxNz4bOy87AdO8OBNpVeSyBS5s9QdRqjQablkEqEWJEWSjvnfPVdJLFLCOMX+1kqOPp55lu0w1qo1l2VqM3FAtukB93oYIvdzv+qAAizA6SMTVUo/sF1MzPbEBZYUPy4HlclIZfLzRJ3bRksUs1lMp48hXn+PJfFc3Uh1JOPr5wj0iZ3bB0BgUtwTNr3KnZpFWw14FmAV06QSwgd736/nVs5nTxhhX/JMpykzZI6J3VrKGoxMw626x3PqNkZlKxJbSBBTEk/JQ2cZ9WKuRzClU7xtW5QjyZI5HEMqcH8fiPquploOCztrpiMjh9OOPRrFb6LRTHeWmu9fnQIV+XmusB" } }, { "type": "interim", "title": "General solutions for $$\\sin\\left(x+\\frac{π}{4}\\right)=-\\frac{\\sqrt{2}}{2}$$", "result": "x+\\frac{π}{4}=\\frac{5π}{4}+2πn,\\:x+\\frac{π}{4}=\\frac{7π}{4}+2πn", "steps": [ { "type": "step", "primary": "$$\\sin\\left(x\\right)$$ periodicity table with $$2πn$$ cycle:<br/>$$\\begin{array}{|c|c|c|c|}\\hline x&\\sin(x)&x&\\sin(x)\\\\\\hline 0&0&π&0\\\\\\hline \\frac{π}{6}&\\frac{1}{2}&\\frac{7π}{6}&-\\frac{1}{2}\\\\\\hline \\frac{π}{4}&\\frac{\\sqrt{2}}{2}&\\frac{5π}{4}&-\\frac{\\sqrt{2}}{2}\\\\\\hline \\frac{π}{3}&\\frac{\\sqrt{3}}{2}&\\frac{4π}{3}&-\\frac{\\sqrt{3}}{2}\\\\\\hline \\frac{π}{2}&1&\\frac{3π}{2}&-1\\\\\\hline \\frac{2π}{3}&\\frac{\\sqrt{3}}{2}&\\frac{5π}{3}&-\\frac{\\sqrt{3}}{2}\\\\\\hline \\frac{3π}{4}&\\frac{\\sqrt{2}}{2}&\\frac{7π}{4}&-\\frac{\\sqrt{2}}{2}\\\\\\hline \\frac{5π}{6}&\\frac{1}{2}&\\frac{11π}{6}&-\\frac{1}{2}\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "x+\\frac{π}{4}=\\frac{5π}{4}+2πn,\\:x+\\frac{π}{4}=\\frac{7π}{4}+2πn" } ], "meta": { "interimType": "Trig General Solutions sin 1Eq" } }, { "type": "interim", "title": "Solve $$x+\\frac{π}{4}=\\frac{5π}{4}+2πn:{\\quad}x=2πn+π$$", "input": "x+\\frac{π}{4}=\\frac{5π}{4}+2πn", "steps": [ { "type": "interim", "title": "Move $$\\frac{π}{4}\\:$$to the right side", "input": "x+\\frac{π}{4}=\\frac{5π}{4}+2πn", "result": "x=2πn+π", "steps": [ { "type": "step", "primary": "Subtract $$\\frac{π}{4}$$ from both sides", "result": "x+\\frac{π}{4}-\\frac{π}{4}=\\frac{5π}{4}+2πn-\\frac{π}{4}" }, { "type": "interim", "title": "Simplify", "input": "x+\\frac{π}{4}-\\frac{π}{4}=\\frac{5π}{4}+2πn-\\frac{π}{4}", "result": "x=2πn+π", "steps": [ { "type": "interim", "title": "Simplify $$x+\\frac{π}{4}-\\frac{π}{4}:{\\quad}x$$", "input": "x+\\frac{π}{4}-\\frac{π}{4}", "steps": [ { "type": "step", "primary": "Add similar elements: $$\\frac{π}{4}-\\frac{π}{4}=0$$" }, { "type": "step", "result": "=x" } ], "meta": { "interimType": "Generic Simplify Specific 1Eq" } }, { "type": "interim", "title": "Simplify $$\\frac{5π}{4}+2πn-\\frac{π}{4}:{\\quad}2πn+π$$", "input": "\\frac{5π}{4}+2πn-\\frac{π}{4}", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=2πn-\\frac{π}{4}+\\frac{5π}{4}" }, { "type": "interim", "title": "Combine the fractions $$-\\frac{π}{4}+\\frac{5π}{4}:{\\quad}π$$", "result": "=2πn+π", "steps": [ { "type": "step", "primary": "Apply rule $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{-π+5π}{4}" }, { "type": "step", "primary": "Add similar elements: $$-π+5π=4π$$", "result": "=\\frac{4π}{4}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{4}{4}=1$$", "result": "=π" } ], "meta": { "interimType": "LCD Top Title 1Eq" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vDfH68okH1ds8y2ydvKfCWcFFpoJdG5SeY0teQk+6FmVgW9NxyVNAwlMGEY4guYYo5FYteSPKwXny4uCMrdsKwFPAxWwXsG6wVjl02ZYROVN5Aod6Hr1Lp2e/29KhSgUgQHNT2nz+ImvmnBFu276+Yv4cPk3yR+xGDi4q183fhMzErW3f+p074F/CjVMUdP+" } }, { "type": "step", "result": "x=2πn+π" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "interim", "title": "Solve $$x+\\frac{π}{4}=\\frac{7π}{4}+2πn:{\\quad}x=2πn+\\frac{3π}{2}$$", "input": "x+\\frac{π}{4}=\\frac{7π}{4}+2πn", "steps": [ { "type": "interim", "title": "Move $$\\frac{π}{4}\\:$$to the right side", "input": "x+\\frac{π}{4}=\\frac{7π}{4}+2πn", "result": "x=2πn+\\frac{3π}{2}", "steps": [ { "type": "step", "primary": "Subtract $$\\frac{π}{4}$$ from both sides", "result": "x+\\frac{π}{4}-\\frac{π}{4}=\\frac{7π}{4}+2πn-\\frac{π}{4}" }, { "type": "interim", "title": "Simplify", "input": "x+\\frac{π}{4}-\\frac{π}{4}=\\frac{7π}{4}+2πn-\\frac{π}{4}", "result": "x=2πn+\\frac{3π}{2}", "steps": [ { "type": "interim", "title": "Simplify $$x+\\frac{π}{4}-\\frac{π}{4}:{\\quad}x$$", "input": "x+\\frac{π}{4}-\\frac{π}{4}", "steps": [ { "type": "step", "primary": "Add similar elements: $$\\frac{π}{4}-\\frac{π}{4}=0$$" }, { "type": "step", "result": "=x" } ], "meta": { "interimType": "Generic Simplify Specific 1Eq" } }, { "type": "interim", "title": "Simplify $$\\frac{7π}{4}+2πn-\\frac{π}{4}:{\\quad}2πn+\\frac{3π}{2}$$", "input": "\\frac{7π}{4}+2πn-\\frac{π}{4}", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=2πn-\\frac{π}{4}+\\frac{7π}{4}" }, { "type": "interim", "title": "Combine the fractions $$-\\frac{π}{4}+\\frac{7π}{4}:{\\quad}\\frac{3π}{2}$$", "result": "=2πn+\\frac{3π}{2}", "steps": [ { "type": "step", "primary": "Apply rule $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{-π+7π}{4}" }, { "type": "step", "primary": "Add similar elements: $$-π+7π=6π$$", "result": "=\\frac{6π}{4}" }, { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=\\frac{3π}{2}" } ], "meta": { "interimType": "LCD Top Title 1Eq" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s721CWpB+GqxmfZ6D5M4rOmmcFFpoJdG5SeY0teQk+6FmVgW9NxyVNAwlMGEY4guYYo5FYteSPKwXny4uCMrdsK9ZI4pcfclnSoUnzr4Mfnw9eTZMykILbMC5S4vTIC/oK7kAjP76qW66lOUsURwT0nXW9I8cIgzrn9At5awiUWKn/jmEQWypabqaffeYmJOZD4NZZ9/znaD8RVZSxoYDkhA==" } }, { "type": "step", "result": "x=2πn+\\frac{3π}{2}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "result": "x=2πn+π,\\:x=2πn+\\frac{3π}{2}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\sin(x)+\\sin^{2}(x)+\\cos(x)+\\cos^{2}(x)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }