Question

On what intervals within [0, 2π) is f increasing? (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
y=sin(x+pi/4)

Answer 1

graph looks just like \(y=\sin(x)\) but shifted left \(\frac{\pi}{4}\)

Answer 2

sin is increasing on \((0,\frac{\pi}{2})\) so this one is increasing on \((-\frac{\pi}{4},\frac{\pi}{4})\)
sine is also increasing on \((\frac{3\pi}{2},\frac{5\pi}{2})\) so this one is increasing on \((\frac{5\pi}{4}, \frac{9\pi}{4})\)

Answer 3

but if you are only in the interval \((0, 2\pi)\) the answer would be
\[(0,\frac{\pi}{4})\] and
\[(\frac{5\pi}{4},2\pi)\]

Answer 4

Thank you)

Answer 5

yw