### Home > PC3 > Chapter 2 > Lesson 2.3.3 > Problem2-156

2-156.

​Graph at least two complete cycles of each of the following functions.

Sketch a general curve first (with shifting), then scale the axes to match the amplitude and/or period.

1. $y=5\sin(3x)$

The period is $\frac{2\pi}{3}$.

1. $y=\cos(\pi x)​$

The period is $\frac{2\pi}{\pi}$.

1. $y=\sin\left(\frac{\pi x}{5}\right)$

The period is $10$.

1. $y=\cos\left(\frac{\pi x}{5}\right)+3$

Start by sketching a cosine graph that has been shifted up $3$ units.