considering the following function,
f(x) = -7 cos(x/2 + pi)
what would be the amplitude of the function?
what would be the exact period of f(x) (in radians)?
thanks for your help.
2007-03-15 21:02:04 · 7 answers · asked by zz06 3 in Science & Mathematics ➔ Mathematics
Amplitude is 7. This is simply the absolute value of the number that is multiplied by the cos function.
The period is 4pi. You should know that the period of the standard cos function is 2pi. The pi term in the parenthesis does not affect the period and neither does the amplitude. So to make this easier, we will just compare cos(x) and cos(x/2). The cos(x) has a period of 2pi, meaning cos(0) and cos(2pi) are the same. Also, the two functions are equal at x=0. To figure out the period of cos(x/2), we just need to set x/2=2pi and solve for x, which is 4pi. Or you can just memorize the properties of the function.
2007-03-15 21:21:23 · answer #1 · answered by Milton's Fan 3 · 0⤊ 0⤋
Amplitude for a sin or cos wave is always the constant before the funtion, without regard to positive or negative...
so, in your case, the amplitude is 7.
the period of a standard cos(x) is 2pi, but since you have (x/2) your period is going to double (hence the 1/2 *x)
in general cos ( fraction * x ) means the period gets bigger by a factor of the fraction
cos ( |#| > 1 * x ) means the period shrinks by a factor of the number.... ie, if you have cos (10x) the period is 10 times smaller...if you have cos (1/10 x) the period is 10 times bigger.
a general rule for sines and cosines is the following, dont feel bad if you dont get it, but its a way to identify how the graph should look.....
from sin (x) all of the modifications are as follows:
A sin ( B x + C) + D
A - D is the amplitude (usually A, but you must subtract D if the graph has a vertical shift)
B is the factor that the period changes by (covered above)
C is the horizontal shift of the graph ( usually some fraction of pi)
D is the vertical shift of the graph ( usually integer values)
hope this helps you out, if not feel free to post more...I love Trig!
2007-03-16 04:19:49 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The amplitude is 7.
The period is 4pi.
2007-03-16 04:20:43 · answer #3 · answered by cabadbaranon 1 · 0⤊ 0⤋
amplitude 7.
period 4pi
2007-03-16 04:09:42 · answer #4 · answered by gjmb1960 7 · 1⤊ 0⤋
Amplitude = 7
Graph repeats every 720° = 4Ï radians
period = 4Ï radians
2007-03-16 07:33:48 · answer #5 · answered by Como 7 · 0⤊ 0⤋
amplitude: 7 ( and the graph would be flipped upside down)
period: 4pi
2007-03-16 04:20:27 · answer #6 · answered by lalala:) 1 · 0⤊ 0⤋
amplitude = 7
period = 0.4Ï = 2Ï/5
2007-03-16 04:22:39 · answer #7 · answered by math freak 3 · 0⤊ 1⤋