Trigonometry and Modelling

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Question 37
Medium
i.

Determine the phase angles ϕ\phiϕ, in the range −60∘<ϕ<60∘-60^\circ < \phi < 60^\circ−60∘<ϕ<60∘, that satisfy the following equilibrium condition for a mechanical oscillator:

5sin⁡(3ϕ+10∘)+2cos⁡(3ϕ+10∘)=05 \sin(3\phi + 10^\circ) + 2 \cos(3\phi + 10^\circ) = 05sin(3ϕ+10∘)+2cos(3ϕ+10∘)=0

giving your answers to one decimal place.

[4]
ii.

A periodic voltage signal V V\,V follows the model

5sin⁡2t−8cos⁡t=25 \sin^2 t - 8 \cos t = 25sin2t−8cost=2

Find all values of t t\,t in the range 0<t<2π 0 < t < 2\pi\,0<t<2π for which this model holds, giving your answers to 3 significant figures.

[5]

Trigonometry and Modelling Questions

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