sec(-(7pi)/2)

{ "query": { "display": "$$\\sec\\left(-\\frac{7π}{2}\\right)$$", "symbolab_question": "TRIG_EVALUATE#\\sec(-\\frac{7π}{2})" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\mathrm{Undefined}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sec\\left(-\\frac{7π}{2}\\right)=$$Undefined", "input": "\\sec\\left(-\\frac{7π}{2}\\right)", "steps": [ { "type": "step", "primary": "Use the following property: $$\\sec\\left(-x\\right)=\\sec\\left(x\\right)$$", "secondary": [ "$$\\sec\\left(-\\frac{7π}{2}\\right)=\\sec\\left(\\frac{7π}{2}\\right)$$" ], "result": "=\\sec\\left(\\frac{7π}{2}\\right)" }, { "type": "interim", "title": "$$\\sec\\left(\\frac{7π}{2}\\right)=\\sec\\left(\\frac{3π}{2}\\right)$$", "input": "\\sec\\left(\\frac{7π}{2}\\right)", "result": "=\\sec\\left(\\frac{3π}{2}\\right)", "steps": [ { "type": "step", "primary": "Rewrite $$\\frac{7π}{2}$$ as $$2π+\\frac{3π}{2}$$", "result": "=\\sec\\left(2π+\\frac{3π}{2}\\right)" }, { "type": "step", "primary": "Apply the periodicity of $$\\sec$$: $$\\sec\\left(x+2π\\right)=\\sec\\left(x\\right)$$", "secondary": [ "$$\\sec\\left(2π+\\frac{3π}{2}\\right)=\\sec\\left(\\frac{3π}{2}\\right)$$" ], "result": "=\\sec\\left(\\frac{3π}{2}\\right)" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "Rewrite using trig identities:$${\\quad}$$Undefined", "input": "\\sec\\left(\\frac{3π}{2}\\right)", "result": "=\\mathrm{Undefined}", "steps": [ { "type": "step", "primary": "Use the basic trigonometric identity: $$\\sec\\left(x\\right)=\\frac{1}{\\cos\\left(x\\right)}$$", "result": "=\\frac{1}{\\cos\\left(\\frac{3π}{2}\\right)}" }, { "type": "interim", "title": "Simplify $$\\frac{1}{\\cos\\left(\\frac{3π}{2}\\right)}:{\\quad}$$Undefined", "input": "\\frac{1}{\\cos\\left(\\frac{3π}{2}\\right)}", "result": "=\\mathrm{Undefined}", "steps": [ { "type": "step", "primary": "$$\\cos\\left(\\frac{3π}{2}\\right)=0$$", "result": "=\\frac{1}{0}" }, { "type": "step", "primary": "$$\\frac{x}{0}\\:$$is undefined", "result": "=\\mathrm{Undefined}" } ], "meta": { "solvingClass": "Solver", "interimType": "Algebraic Manipulation Simplify Title 1Eq" } } ], "meta": { "interimType": "Trig Rewrite Using Trig identities Title 0Eq" } } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }