SOLUTION: Use a reference rectangle and the rule of fourths to draw an accurate sketch of the following function through at least one full cycle.
y = cos(4t)
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-> SOLUTION: Use a reference rectangle and the rule of fourths to draw an accurate sketch of the following function through at least one full cycle.
y = cos(4t)
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Question 1083715: Use a reference rectangle and the rule of fourths to draw an accurate sketch of the following function through at least one full cycle.
y = cos(4t)
period = 2pi / frequency = 2pi / 4 = 2pi/4 = pi/2.
the full cycle of the cosine function of y = cos(4t) goes from 0 to pi/2.
if you break the period into quarters, you will get quarter periods of pi/2 / 4 = pi/8.
the function starts at x = 0
the first quarter ends at pi/8
the second quarter ends at 2pi/8
the third quarter ends at 3pi/8
the fourth quarter ends at 4pi/8
simplify the fractions and you get:
the function starts at x = 0
the first quarter ends at pi/8
the second quarter ends at pi/4
the third quarter ends at 3pi/8
the fourth quarter ends at pi/2
your rectangle has vertical sides at x = 0 and x = pi/2.
your rectangle has horizontal sides at y = 1 and y = -1.
here's the graph of cos(4x).
x is used instead of 5 to satisfy the graphing software.
here's a reference on graphing of sine and cosine functions.
