How do you use the amplitude and period to graph #y = –3 cos(2θ + 45°) + 3 #?

1 Answer
bp
Apr 30, 2016

Amplitude 3, period #pi#

Explanation:

General form of a sinusoidal (or sine wave) function is#y=A sin(Bx-C)+D#
Where |A| is the amplitude, period is #(2pi)/B# Phase shift is #C/B# and D is the vertical shift.
Now in the given function instead of sine it is cos. Hence we change it by wrting cosx as #sin (x+pi/2)#

The given function can thus be written as #y= -3 sin(2theta+45^o +90^o) +3#
0r #y= -3sin(2theta+(3pi)/4) +3#

Thus amplitude would be 3 and period would be #(2pi)/2# or, #pi#

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