To create clear graphs of trigonometric functions, you can use some helpful methods:

1. Important Features:

   • Amplitude: In the equation $y = A \sin(Bx + C) + D$, the amplitude is the absolute value of $A$. This tells us how tall the waves will be.
   • Period: The period shows how long it takes for the wave to repeat. You can find it using the formula $\frac{2\pi}{|B|}$.
   • Phase Shift: This tells you how much the wave moves left or right. It's found with $-\frac{C}{B}$.
   • Vertical Shift: This is how much the wave moves up or down, and it's based on the value of $D$.

2. Making a Table:

   • Create a table with important angles like $0$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, and $\frac{\pi}{2}$. Use these angles to find the matching $y$ values.

3. Plotting Points:

   • Take the points from your table and plot them on a coordinate plane. Remember to keep the waves balanced because they have a repeating pattern.

By using these methods, you can create accurate and clear graphs of trigonometric functions!