Periodicity plays a big role in how sine and cosine functions act. These functions are called periodic because they repeat their patterns over a set distance.

1. What is a Period?

• The main period for the sine function, written as ( y = \sin(x) ), is ( 2\pi ).
• The main period for the cosine function, written as ( y = \cos(x) ), is also ( 2\pi ).

2. How They Look on a Graph:

• Both functions start to repeat their values every ( 2\pi ) radians. This leads to steady wave patterns.
• For example, ( y = \sin(x) ) is the same as ( y = \sin(x + 2\pi k) ). Here, ( k ) can be any whole number.

3. What is Amplitude?

• Amplitude is the tallest point of the wave from the center line.
• For the basic sine and cosine functions, the amplitude stays the same at ( 1 ). This doesn’t change, even though they repeat their patterns.

Getting to know these features is really important for understanding and drawing sine and cosine functions well.