sin(θ_{1})=-10/13

{ "query": { "display": "$$\\sin\\left(θ_{1}\\right)=-\\frac{10}{13}$$", "symbolab_question": "EQUATION#\\sin(θ_{1})=-\\frac{10}{13}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "θ_{1}=-0.87763…+2πn,θ_{1}=π+0.87763…+2πn", "degrees": "θ_{1}=-50.28486…^{\\circ }+360^{\\circ }n,θ_{1}=230.28486…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(θ_{1}\\right)=-\\frac{10}{13}{\\quad:\\quad}θ_{1}=-0.87763…+2πn,\\:θ_{1}=π+0.87763…+2πn$$", "input": "\\sin\\left(θ_{1}\\right)=-\\frac{10}{13}", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(θ_{1}\\right)=-\\frac{10}{13}", "result": "θ_{1}=\\arcsin\\left(-\\frac{10}{13}\\right)+2πn,\\:θ_{1}=π+\\arcsin\\left(\\frac{10}{13}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(θ_{1}\\right)=-\\frac{10}{13}$$", "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_{1}=\\arcsin\\left(-\\frac{10}{13}\\right)+2πn,\\:θ_{1}=π+\\arcsin\\left(\\frac{10}{13}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "θ_{1}=-0.87763…+2πn,\\:θ_{1}=π+0.87763…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "θ_{1}", "plotRequest": "\\sin(θ_{1})+\\frac{10}{13}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }