which statement is not true about the function y=cos(x)? ?
a. The amplitude can be found by dividing the vertical distance between (0,1) and (pi,-1) by 2.
b. The amplitude can be found by determining the vertical distance from a maximum point to the x-ais.
c. The period can be found by determining the horizontal distance between any two consecutive x-intercepts.
d. The period can be found by determining the horizontal distance between (0,1) and (2pi,1)
I think 'b' is definitely not the answer.
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Answers & Comments
They are all true, but (c) is a little "less" true, in that the horizontal distance between two consecutive x-intercepts is only half the period. The period can indeed be FOUND by determining the distance between two consecutive x-intercepts, but then you'd have to multiply that distance by 2.
So I vote for (c) as the "not true" statement.
(c) is wrong. The cosine function is zero ("has x intercepts") *twice* in each period. The intercept values are equally-spaced, so the distance between consecutive x intercepts is half a wavelength (or half a period.)
A couple of notes:
"Period" usually applies to a function of time, and that would normally be written as y = cos t instead of y = cos x.
The function y = cos x has a well-known amplitude of 1 and period of 2*pi, so you don't really need to "determine it." Scale factors inside and outside the cosine change these, where y = a cos (wt) has amplitude |a| and period 2*pi*w.