How do you find the amplitude and period of #y=2sec(4/5theta)#?

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1 Answer
mimi
Jun 24, 2017

Amplitude is #2#.
Period is #(5pi)/2# or #7.85398163#.

Explanation:

Standard Form: #y=asecb(x-c)+d#
Equation: #y=2sec(4/5theta)#
#a=2#
#b=4/5#
#c=#none
#d=#none

AMPLITUDE
amplitude = distance from middle of graph (y=0) to highest and lowest points on graph
formula: #|a|#
#|2|#
#2#
Amplitude is #2#.

PERIOD
period = interval in which the graph repeats itself
formula: #(2pi)/|b|#
#(2pi)/|4/5|#
#(2pi)/(4/5)#
#2pi-:4/5#
#2pi*5/4#
#(10pi)/4#
#(5pi)/2 = 7.85398163#
Period is #(5pi)/2# or #7.85398163#.

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