How do you find the amplitude and period of #f(x) = -7 cos(x/2 + pi) #?

1 Answer
Gió
Jul 4, 2015

Amplitude is #7#
Period is #4pi#

Explanation:

You must use the coefficients in front of #cos# and #x#:
1] Amplitude is #7# (the modulus of the coefficient #-7#), in this case your #cos# oscillates between #+7# and #-7#;
2] For the period you use the #1/2# in front of #x# in the argument of #cos# as:
#period=(2pi)/color(red)(1/2)# so your period will be #4pi=12.6#.
Graphically you can see these values as:
graph{-7cos(x/2+pi) [-9.93, 10.07, -4.27, 5.73]}

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