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Answer 1 · 2016-10-04T16:36:03

The function representing the variation of voltage with time is given by

#V(t)=60sin(2t+0.8)," where "t>=0#

(a) As it is a sine function , It will have

(1) a maximum value
when #sin(2t+0.8)# is maximum = 1
So maximum value #V(t)=60V#

(2) a minimum value
when #sin(2t+0.8)# is maximum =-1

So minimum value #V(t)=-60V#

(b) we are to findout the time when first time #V(t)=30V#

So putting #V(t)=30V# we get

#30=60sin(2t+0.8)#

#=>sin(2t+0.8)=30/60=1/2=sin(pi/6)#

#=>2t=pi/6-0.8#

#=>2t=3.14/6=-0.8<0->"not possible"#

So taking

#sin(2t+0.8)=sin(pi-pi/6)#

#=>2t=(5pi)/6=-0.8=(5xx3.14)/6-0.8#

#=>2t=1.82#

#t=0.91s#

Hence first time at 0.91s #V(t)# will reach to 30V value