The diagram below shows a sinusoidal curve. The equation of the curve will be

Question

Infinity Learn · Accepted Answer

Let T be the time period; then $$T2=5$$$$π$$$$64$$−π$$64=4$$$$π$$$$64T=$$π$$8s$$ ∴ω$$=2$$$$π$$$$T=2$$π$$($$π$$/8)=16rad/sAlso$$, A $$=$$ $$10$$ cm (from$$ the $$graph)The$$ equation of the sinusoidal wave can be written as $$y=10sin$$⁡$$(16t+$$ϕ$$), where ϕ is the initial phase.From the graph, corresponding to the crest $$=$$ $$10$$ cm; when $$t=3$$π$$/64$$.    $$10cm=10sin$$⁡$$163$$$$π$$$$64+$$ϕcm    $$sin$$⁡$$3$$$$π$$$$4+$$ϕ$$=1$$  or  $$3$$$$π$$$$4+$$ϕ$$=$$π$$2$$⇒ϕ$$=$$−π$$4$$∴     $$y=10sin$$⁡$$16t$$−π$$4$$

The diagram below shows a sinusoidal curve. The equation of the curve will be

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