cos(x)= 8/13

{ "query": { "display": "$$\\cos\\left(x\\right)=\\frac{8}{13}$$", "symbolab_question": "EQUATION#\\cos(x)=\\frac{8}{13}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=0.90792…+2πn,x=2π-0.90792…+2πn", "degrees": "x=52.02012…^{\\circ }+360^{\\circ }n,x=307.97987…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\cos\\left(x\\right)=\\frac{8}{13}{\\quad:\\quad}x=0.90792…+2πn,\\:x=2π-0.90792…+2πn$$", "input": "\\cos\\left(x\\right)=\\frac{8}{13}", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cos\\left(x\\right)=\\frac{8}{13}", "result": "x=\\arccos\\left(\\frac{8}{13}\\right)+2πn,\\:x=2π-\\arccos\\left(\\frac{8}{13}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cos\\left(x\\right)=\\frac{8}{13}$$", "secondary": [ "$$\\cos\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arccos\\left(a\\right)+2πn,\\:\\quad\\:x=2π-\\arccos\\left(a\\right)+2πn$$" ], "result": "x=\\arccos\\left(\\frac{8}{13}\\right)+2πn,\\:x=2π-\\arccos\\left(\\frac{8}{13}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "x=0.90792…+2πn,\\:x=2π-0.90792…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\cos(x)-\\frac{8}{13}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }