3/8 =cos(θ)

{ "query": { "display": "$$\\frac{3}{8}=\\cos\\left(θ\\right)$$", "symbolab_question": "EQUATION#\\frac{3}{8}=\\cos(θ)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=1.18639…+2πn,θ=2π-1.18639…+2πn", "degrees": "θ=67.97568…^{\\circ }+360^{\\circ }n,θ=292.02431…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{3}{8}=\\cos\\left(θ\\right){\\quad:\\quad}θ=1.18639…+2πn,\\:θ=2π-1.18639…+2πn$$", "input": "\\frac{3}{8}=\\cos\\left(θ\\right)", "steps": [ { "type": "step", "primary": "Switch sides", "result": "\\cos\\left(θ\\right)=\\frac{3}{8}" }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\cos\\left(θ\\right)=\\frac{3}{8}", "result": "θ=\\arccos\\left(\\frac{3}{8}\\right)+2πn,\\:θ=2π-\\arccos\\left(\\frac{3}{8}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\cos\\left(θ\\right)=\\frac{3}{8}$$", "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(\\frac{3}{8}\\right)+2πn,\\:θ=2π-\\arccos\\left(\\frac{3}{8}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=1.18639…+2πn,\\:θ=2π-1.18639…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "\\frac{3}{8}-\\cos(θ)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }