sin(θ)= 12/20

{ "query": { "display": "$$\\sin\\left(θ\\right)=\\frac{12}{20}$$", "symbolab_question": "EQUATION#\\sin(θ)=\\frac{12}{20}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=0.64350…+2πn,θ=π-0.64350…+2πn", "degrees": "θ=36.86989…^{\\circ }+360^{\\circ }n,θ=143.13010…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(θ\\right)=\\frac{12}{20}{\\quad:\\quad}θ=0.64350…+2πn,\\:θ=π-0.64350…+2πn$$", "input": "\\sin\\left(θ\\right)=\\frac{12}{20}", "steps": [ { "type": "step", "primary": "Cancel the common factor: $$4$$", "result": "\\sin\\left(θ\\right)=\\frac{3}{5}" }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(θ\\right)=\\frac{3}{5}", "result": "θ=\\arcsin\\left(\\frac{3}{5}\\right)+2πn,\\:θ=π-\\arcsin\\left(\\frac{3}{5}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(θ\\right)=\\frac{3}{5}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+2πn,\\:\\quad\\:x=π-\\arcsin\\left(a\\right)+2πn$$" ], "result": "θ=\\arcsin\\left(\\frac{3}{5}\\right)+2πn,\\:θ=π-\\arcsin\\left(\\frac{3}{5}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=0.64350…+2πn,\\:θ=π-0.64350…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ", "plotRequest": "\\sin(θ)-\\frac{12}{20}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }