Question #c8ed2

1 Answer
Monzur R.
May 27, 2017

#12sinvartheta+5cosvartheta=13sin(vartheta+0.394)#

Explanation:

#12sinvartheta+5cosvartheta=rsin(vartheta+varphi)#

#rsin(vartheta+varphi)=rsinvarthetacosvarphi+rcosvarthetasinvarphi#

Comparing coefficients, we find that #rsinvarphi=5# and #rcosvarphi=12#

#tanvarphi=(rsinvarphi)/(rcosvarphi)=5/12#

#varphi=arctan(5/12)=0.394^"rad"#

Since neither the unit of angular measurement nor accuracy were specified, I am using the standard unit of angular measurement, radians, and 3 sf. for accuracy.

#r=sqrt(sin^2varphi+cos^2varphi)=sqrt(5^2+12^2)=13#

#therefore12sinvartheta+5cosvartheta=13sin(vartheta+0.394)#

I shall leave ii) for another contributor

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