When you look at the graphs of trigonometric functions, there are some important features that make it easier to see how these functions work. Let’s break it down step by step:

Periodicity

1. What is Periodicity?
   Trigonometric functions like sine (written as $\sin x$) and cosine (written as $\cos x$) are periodic. This means they repeat their values over and over in regular patterns. For sine and cosine, this pattern repeats every $2\pi$ units.

2. Tangent and Cotangent:
   These functions are a bit different. They have a repetition of $\pi$ instead. This is why their graphs look different from sine and cosine!

Amplitude

1. What is Amplitude?
   The amplitude is the distance from the middle of the graph to its highest point (the peak) or lowest point (the trough).

2. For Sine and Cosine:
   In functions like $y = A \sin x$ or $y = A \cos x$, the amplitude is the absolute value of $A$. For example, if $A = 3$, then the graph goes up to 3 units above and 3 units below the middle line.

3. Tangent:
   The tangent function doesn’t have a defined amplitude because it can get really big, even approaching infinity.

Other Features

• Midline:
  The midline is the horizontal line that the graph moves up and down around. For most basic sine and cosine functions, the midline is at $y = 0$.

• Phase Shift:
  This means moving the graph left or right. You can spot a phase shift by looking for changes in the formula, like in $y = A \sin(B(x - C))$.

By understanding these features, you can sketch and analyze these graphs more easily!