sin(θ)=-(sqrt(7))/4

{ "query": { "display": "$$\\sin\\left(θ\\right)=-\\frac{\\sqrt{7}}{4}$$", "symbolab_question": "EQUATION#\\sin(θ)=-\\frac{\\sqrt{7}}{4}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ=-0.72273…+2πn,θ=π+0.72273…+2πn", "degrees": "θ=-41.40962…^{\\circ }+360^{\\circ }n,θ=221.40962…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(θ\\right)=-\\frac{\\sqrt{7}}{4}{\\quad:\\quad}θ=-0.72273…+2πn,\\:θ=π+0.72273…+2πn$$", "input": "\\sin\\left(θ\\right)=-\\frac{\\sqrt{7}}{4}", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(θ\\right)=-\\frac{\\sqrt{7}}{4}", "result": "θ=\\arcsin\\left(-\\frac{\\sqrt{7}}{4}\\right)+2πn,\\:θ=π+\\arcsin\\left(\\frac{\\sqrt{7}}{4}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(θ\\right)=-\\frac{\\sqrt{7}}{4}$$", "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{\\sqrt{7}}{4}\\right)+2πn,\\:θ=π+\\arcsin\\left(\\frac{\\sqrt{7}}{4}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ=-0.72273…+2πn,\\:θ=π+0.72273…+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{\\sqrt{7}}{4}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }