To graph trigonometric functions and solve inequalities, here’s an easy way to do it:

1. Identify the Function: First, figure out which trigonometric function you have. It could be sine, cosine, or tangent. For this example, let’s use $y = \sin(x)$.

2. Draw the Basic Graph: Next, sketch the basic graph of the function. For sine, you usually draw it from $0$ to $2\pi$.

3. Mark Key Points: Look for important points on the graph where the function reaches high or low values and when it crosses the x-axis. For $y = \sin(x)$, the key points are:

   • $(0,0)$
   • $(\frac{\pi}{2}, 1)$
   • $(\pi, 0)$
   • $(\frac{3\pi}{2}, -1)$
   • $(2\pi, 0)$

4. Set Up the Inequality: If you want to solve something like $\sin(x) > 0$, you’re checking where the graph is above the x-axis.

5. Shade the Solution Area: On your graph, shade in the parts where the inequality is true. For $\sin(x) > 0$, you would shade the area between $0$ and $\pi$ and again from $2\pi$ to $3\pi$, and so on.

6. Consider the Periodicity: Remember that trigonometric functions repeat. This means there are many answers based on how the function works.

By following these steps, you can easily see where to find solutions for trigonometric inequalities!