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Mathematics 87 Online
zarkam21:

Long- 4,5 part questions (Who's up for the challenge) ^~^

zarkam21:

1 attachment
zarkam21:

1 attachment
Vocaloid:

determining the period of sec/csc function is|dw:1521817537805:dw| little tricky but

Vocaloid:

|dw:1521817544954:dw|

Vocaloid:

it looks like one repeating unit of the question starts at -pi/2 and ends at about pi, what would the period be?

zarkam21:

just count in between right

Vocaloid:

actually just a minute, we would start at -pi/2 and go all the way until the graph extends to -infinity, completing the cycle

Vocaloid:

|dw:1521817743785:dw|

Vocaloid:

|dw:1521817748454:dw|

Vocaloid:

so it's really just -pi/2 to pi/2, then continuing to pi/2 to -pi/2 wrapping around, so adding up all the pieces we get 2pi as the period (this is kind of hard to see but you would sum up the x-values of all the parts since only one period is being represented so yeah period = 2pi

Vocaloid:

anyway, for part II, let's try drawing straight lines where the period starts and ends like so:

Vocaloid:

|dw:1521817914968:dw|

Vocaloid:

so if it the period starts at -pi/6 and ends at 2pi/3 what's the period?

zarkam21:

4

zarkam21:

Ugh

Vocaloid:

the entire period is just ending point - starting point so (2pi/3) - (-pi/6) = ?

zarkam21:

5pi/6

Vocaloid:

actually my mistsake, the period ends at (5pi/6) to be a bit more precise making the period (5pi/6) - (-pi/6) = pi so the period is pi

zarkam21:

okay so for part 3 it would be sec ?

Vocaloid:

yup, I'm not really sure what they'd want for the explanation but you could mention it has the same period as cos, has asymptotes where the zeroes of cos would be, has the same symmetry, etc.

zarkam21:

Got it for part 4 it would be 3?

Vocaloid:

yup, 3 since the new vertex is (0,3)

zarkam21:

for part 5 i'm a little stumped

Vocaloid:

well, if the period changed from 2pi to pi, what coefficient of x would we need to produce a period of pi instead of 2pi?

Vocaloid:

remember: period = 2pi/b where b is the coefficient of x

zarkam21:

2

Vocaloid:

awesome, so the dotted function = sec(2x) which is all they need for part V

zarkam21:

for part 6 i would just use the line right

Vocaloid:

what line

zarkam21:

oh nvm

Vocaloid:

I think we mentioned it before but the solid line is sec(x) so the recprical would be cos(x) = your answer

zarkam21:

Yay thank you

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