Question

What is the phase shift of y = csc2(x + pi/4)?

-pi/2
-pi/4 <<<
pi/4

Answer 1

Compare your function to the general form:\[y=\csc(2(x+\frac{ \pi }{ 4 }))\rightarrow y=\csc(2x+\frac{ \pi }{ 2 })=\csc(bx+c).\]

The period, in such case, is \[\frac{ 2\pi }{ b }\] and the phase shift is \[\frac{ -c }{ b }\] so, with c=pi/2 and b=2, I'd say the phase shift is \[\frac{ -c }{ b }=\frac{ -\frac{ \pi }{ 2 } }{ 2 }=\frac{ -\pi }{ 4 }.\]

Answer 2

@mathmale thanks! i also have a question about this

Answer 3

What is the phase shift of y = cos(3x - 3pi/4)?

pi/4
3pi/4
9pi/4
4π

if i do i divide the 3 from 3x to both cos ^ -3pi/4 or multiply them??

Answer 4

Here I'd identify b as b=3 and c as c=-3pi/4.
Thus, the phase shift would be -c/b. Try that.

Answer 5

how would i calculate -3pi/4 / 3?

Answer 6

\[\frac{ -c }{ b }=\frac{ -(3/4)\pi }{ 3 }=\frac{ -\pi }{ 4 }\]

Answer 7

then the answer be pi/4 correct?!