(sin(42))/(22)=(sin(B))/(12)

{ "query": { "display": "$$\\frac{\\sin\\left(42^{\\circ\\:}\\right)}{22}=\\frac{\\sin\\left(B\\right)}{12}$$", "symbolab_question": "EQUATION#\\frac{\\sin(42^{\\circ })}{22}=\\frac{\\sin(B)}{12}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "B=0.37361…+360^{\\circ }n,B=180^{\\circ }-0.37361…+360^{\\circ }n", "radians": "B=0.37361…+2πn,B=π-0.37361…+2πn", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{\\sin\\left(42^{\\circ\\:}\\right)}{22}=\\frac{\\sin\\left(B\\right)}{12}{\\quad:\\quad}B=0.37361…+360^{\\circ\\:}n,\\:B=180^{\\circ\\:}-0.37361…+360^{\\circ\\:}n$$", "input": "\\frac{\\sin\\left(42^{\\circ\\:}\\right)}{22}=\\frac{\\sin\\left(B\\right)}{12}", "steps": [ { "type": "step", "primary": "Switch sides", "result": "\\frac{\\sin\\left(B\\right)}{12}=\\frac{\\sin\\left(42^{\\circ\\:}\\right)}{22}" }, { "type": "interim", "title": "Multiply both sides by $$12$$", "input": "\\frac{\\sin\\left(B\\right)}{12}=\\frac{\\sin\\left(42^{\\circ\\:}\\right)}{22}", "result": "\\sin\\left(B\\right)=\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}", "steps": [ { "type": "step", "primary": "Multiply both sides by $$12$$", "result": "\\frac{12\\sin\\left(B\\right)}{12}=\\frac{12\\sin\\left(42^{\\circ\\:}\\right)}{22}" }, { "type": "step", "primary": "Simplify", "result": "\\sin\\left(B\\right)=\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}" } ], "meta": { "interimType": "Multiply Both Sides Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYk9EJe/h8nombXWbaz3uQ3mv5auhZc6RaLnq70O2bAy9QJwZJaU2KNsU/PvTbTqchD2L2gC9/0Z1Vc1tHdjgVurehDFAC2FmLCpjOb9PI4KDmiaZFISq1AlGzF8ywHBWVpIjlGM9GKH213pGTWYn0b1cMMDZS3+q+G4MQf+V0ZMSJwDJ0u2STxyZMJrzlxx0pK0x+gh9gH6MihK9Pv1MXvnGaMZJe1ygjX89AS02/C9X3RaWPPkyUFEYdpRLdINt+NeleFwwKnR+2qwOXc78ohyieBDlEje6JiWj93nNgROXFZPLdk8I4fs46fXZWE3KPxoMEmyHHeSYz/3dSrgm1veMw0n9r4f4vt7OHDv6CsGctaysPu9leNS4MXgjnnClznyL7URSLQlHzu9g25SQ76+moN+fZySAkjcUdbHZIiWA8LfSxJ+0AgVLpCSnLX0iSl4KtINCsf/apTfW1vkMmmnHl709NPzQqF53hRPr+fMe" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(B\\right)=\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}", "result": "B=\\arcsin\\left(\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}\\right)+360^{\\circ\\:}n,\\:B=180^{\\circ\\:}-\\arcsin\\left(\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}\\right)+360^{\\circ\\:}n", "steps": [ { "type": "step", "primary": "General solutions for $$\\sin\\left(B\\right)=\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}$$", "secondary": [ "$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+360^{\\circ\\:}n,\\:\\quad\\:x=180^{\\circ\\:}-\\arcsin\\left(a\\right)+360^{\\circ\\:}n$$" ], "result": "B=\\arcsin\\left(\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}\\right)+360^{\\circ\\:}n,\\:B=180^{\\circ\\:}-\\arcsin\\left(\\frac{6\\sin\\left(42^{\\circ\\:}\\right)}{11}\\right)+360^{\\circ\\:}n" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "step", "primary": "Show solutions in decimal form", "result": "B=0.37361…+360^{\\circ\\:}n,\\:B=180^{\\circ\\:}-0.37361…+360^{\\circ\\:}n" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "B", "plotRequest": "\\frac{\\sin(42^{\\circ })}{22}-\\frac{\\sin(B)}{12}" }, "showViewLarger": true } }, "meta": { "showVerify": true } }