When you're trying to solve trigonometric inequalities, there are some good tricks that can make things easier. Here’s what I usually find helpful:

1. Know the Inequality: First, it's important to really understand the inequality you're working with. Whether it's something like $\sin(x) > 0$ or $\cos(x) \leq 1$, knowing what the function does and how it repeats is super important.

2. Draw a Graph: I think drawing the graph of the trigonometric function can really help. It allows you to see where the function is above or below a certain value. For instance, if you look at $\sin(x) > 0$, drawing it helps you notice that it’s positive in certain sections like $(0, \pi)$ during each cycle.

3. Know Key Angles: Getting familiar with important angles can also be very helpful. You can use key angles (like $0$, $\frac{\pi}{2}$, $\pi$, etc.) to find out where the function crosses the axes or reaches important values. This helps you notice the intervals more easily.

4. Transform Into Equations: Sometimes, changing the inequality into an equation can make things clearer. For example, if you want to solve $\tan(x) < 1$, you can change it to $\tan(x) - 1 < 0$ and first figure out where $\tan(x) = 1$. This gives you starting points to work from.

5. Don't Forget About Repeats: Finally, remember that trigonometric functions repeat! After you find the basic solutions, make sure to add the period (like $2\pi k$, where $k$ is any whole number) to find all possible solutions.

Using these tips will give you a strong way to tackle trigonometric inequalities easily!