shift f(x)=6cos(3x+pi/2) — step-by-step solution

Let's find the phase shift of

6 \cdot \cos (3 x + \frac{π}{2})

For

a \cdot \cos (b x + c) + d

, write

b x + c = b \cdot (x + \frac{c}{b})

: the graph of

a \cdot \cos (b x) + d

is shifted horizontally by

- \frac{c}{b}

Here the angle is

3 x + \frac{π}{2}

: b =

3

and c =

\frac{π}{2}

, so the phase shift is -c/b =

- \frac{\frac{π}{2}}{3}

- \frac{π}{6}

- \frac{π}{6}

< 0: the graph is shifted

\frac{π}{6}

to the left

▶Phase shift:

- \frac{π}{6}