What is the period of #f(theta)= sin 6 t - cos t #?

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Answer 1 · 2016-08-09T16:41:06

#2pi#

The period of both sin kt and cos kt = #2pi/k#.

Here, the period of the term sin 6t is #pi/3# and the period of - cos t

is #2pi#.

The larger #2pi# is direcly 6 X the other period.

So, the period of the combined oscillation is #2pi#.

See how it works.

#f(t+period)=f(t+2pi)#

#=sin (6(t+2pi))-cos(t+2pi)#

#=sin(6t+12pi)-cos t#

#=sin 6t - cos t#

#=f(t)#