zarkam21:
A?
Vocaloid:
that's not quite right if b = the coefficient of x, and period = 2pi/b what would b need to be?
zarkam21:
B
Vocaloid:
good, period = pi/2 = 2pi/b so b = 4 and B is the correct sol'n
zarkam21:
B
Vocaloid:
good
zarkam21:
B
Vocaloid:
good
zarkam21:
5
Vocaloid:
well done
Vocaloid:
honestly I'd just graph these, some of these comparisons are a pain to work w/ by hand
zarkam21:
A and B
Vocaloid:
good
zarkam21:
D
Vocaloid:
hm. check the period again since the period of a tan function is normally pi then the coefficent b would be given by period = pi/b what is b?
zarkam21:
A
Vocaloid:
awesome, A
zarkam21:
B
Vocaloid:
hm, that's not quite, remember sec has a range from (-infinity,-1) U (1,infinity) so adding 2 would make the graph cross (0,3) not (0,2)
Vocaloid:
as a hint, to make it cross (0,2) you would have to do a vertical stretch by 2
zarkam21:
D
zarkam21:
C
Vocaloid:
it can't be a csc function (notice where the asymptotes are) a vertical shift by 2 would be multiplying the entire function by 2
Vocaloid:
take the sec function, apply a vertical stretch by 2, what's the only possibility?
zarkam21:
A
Vocaloid:
good
Vocaloid:
well, for the regular y = cot(x) where are the asymptotes normally?
zarkam21:
B and C
Vocaloid:
hm, I got something a little different cot(x) = cos(x)/sin(x) so cot(x) takes its asymptotes when sin(x) = 0, what values of x would that be?
zarkam21:
Oh A and D
Vocaloid:
hm, that's not quite right sin(x) takes its 0 values when x = n * pi, so every multiple of pi is an asymptote for cot(x) however, the function in the problem is cot(x/2) not cot(x), so the function gets stretched horizontally and takes its asymptote every 2pi so which answers would be included?
zarkam21:
C and D
Vocaloid:
is pi/2 a multiple of 2pi?
zarkam21:
No
Vocaloid:
hint - sin(0) = 0
zarkam21:
I know it has to do with x=2πn
Vocaloid:
good, so what do you get when n = 0?
zarkam21:
0
zarkam21:
B
Vocaloid:
good, so 0, 2pi, -2pi, etc. so B+D
zarkam21:
-7
Vocaloid:
good
zarkam21:
C
Vocaloid:
well done
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