Question

math trig help pls

Answer 1

i got the vertical translation -2

Answer 2

late response, but just in case you still needed help with this

recall that the parent function has vertical asymptotes every pi units starting from 0

because the function in the problem has asymptotes every 2 pi units instead, it got stretched horizontally by a factor of 2. recall that horizontal stretches take the form x/b where b is the stretch factor, so in this case, you'd have csc(1/2 x) instead of csc(x).

you've calculated the vertical translation correctly.

all that's left is to figure out the vertical stretch or compression. let's sketch out the function based on what we know so far, compare it to the parent csc(x) function, and figure out what the vertical stretch is.

Answer 3

based on the data point of the local min on the new function, we can set up

a * csc(1/2 x) - 2 = y

you can plug in the point x = pi and y = 5 and solve for the vertial stretch factor (a). the -2 comes from the vertical translation which you've already calculated.

Answer 4

yes thank you ive already got it