sin(a)= 7/15

{ "query": { "display": "$$\\sin\\left(a\\right)=\\frac{7}{15}$$", "symbolab_question": "EQUATION#\\sin(a)=\\frac{7}{15}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "a=0.48551…+2πn,a=π-0.48551…+2πn", "degrees": "a=27.81813…^{\\circ }+360^{\\circ }n,a=152.18186…^{\\circ }+360^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(a\\right)=\\frac{7}{15}{\\quad:\\quad}a=0.48551…+2πn,\\:a=π-0.48551…+2πn$$", "input": "\\sin\\left(a\\right)=\\frac{7}{15}", "steps": [ { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(a\\right)=\\frac{7}{15}", "result": "a=\\arcsin\\left(\\frac{7}{15}\\right)+2πn,\\:a=π-\\arcsin\\left(\\frac{7}{15}\\right)+2πn", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(a\\right)=\\frac{7}{15}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+2πn,\\:\\quad\\:x=π-\\arcsin\\left(a\\right)+2πn$$" ], "result": "a=\\arcsin\\left(\\frac{7}{15}\\right)+2πn,\\:a=π-\\arcsin\\left(\\frac{7}{15}\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "a=0.48551…+2πn,\\:a=π-0.48551…+2πn" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "a", "plotRequest": "\\sin(a)-\\frac{7}{15}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }