Trigonometric functions, such as sine, cosine, and tangent, can be visualized and understood by examining their graphs. When graphing trigonometric functions, we consider several important properties.

Amplitude: The amplitude of a trigonometric function determines the maximum and minimum values it reaches. For example, the amplitude of the sine function is 1, while the amplitude of the cosine function is also 1.

Period: The period of a trigonometric function is the horizontal length it takes to complete one full cycle. The period of the sine and cosine functions is 2π, while the period of the tangent function is π.

Phase Shift: The phase shift of a trigonometric function determines the horizontal translation of the graph. A positive phase shift shifts the graph to the right, while a negative phase shift shifts it to the left.

To graph a trigonometric function, we start with the basic graph and apply these transformations. Let's take the example of graphing the function y = 2sin(3x + π/4):

• The amplitude of 2 means the maximum and minimum values will be multiplied by 2.
• The period of 2π/3 means one complete cycle will be compressed to a length of 2π/3.
• The phase shift of π/4 means the entire graph will be shifted to the left by π/4.

By applying these transformations, we can accurately graph the given trigonometric function.

Keep practicing and exploring different trigonometric functions to become more comfortable with graphing them!