cos(θ)=0.7071

{ "query": { "display": "$$\\cos\\left(θ\\right)=0.7071$$", "symbolab_question": "EQUATION#\\cos(θ)=0.7071" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=0.78540…+2πn,θ=2π-0.78540…+2πn", "degrees": "θ=45.00054…^{\\circ }+360^{\\circ }n,θ=314.99945…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\cos\\left(θ\\right)=0.7071{\\quad:\\quad}θ=0.78540…+2πn,\\:θ=2π-0.78540…+2πn$$", "input": "\\cos\\left(θ\\right)=0.7071", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cos\\left(θ\\right)=0.7071", "result": "θ=\\arccos\\left(0.7071\\right)+2πn,\\:θ=2π-\\arccos\\left(0.7071\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cos\\left(θ\\right)=0.7071$$", "secondary": [ "$$\\cos\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arccos\\left(a\\right)+2πn,\\:\\quad\\:x=2π-\\arccos\\left(a\\right)+2πn$$" ], "result": "θ=\\arccos\\left(0.7071\\right)+2πn,\\:θ=2π-\\arccos\\left(0.7071\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=0.78540…+2πn,\\:θ=2π-0.78540…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "\\cos(θ)-0.7071" }, "showViewLarger": true } }, "meta": { "showVerify": true } }