periodicity of y=-4sin(6x+pi/2) — step-by-step solution

We add the definition:

y = -4 \cdot \sin (6 x + \frac{π}{2})

Let's find the smallest positive period of

-4 \cdot \sin (6 x + \frac{π}{2})

For

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

, the period is

T = 2 \cdot \frac{π}{abs (b)}

. The nonzero factor a and the shifts c and d do not change the period

The period of

\sin (x)

2 π

radians

The coefficient of

x

6 x + \frac{π}{2}

6

T = \frac{2 π}{6}

▶Period:

\frac{π}{3}

The numeric value of:

\frac{π}{3}

is:

\frac{\approx 3.1416}{3}

▷

\approx 1.0472