Meet your best friend – the unit circle! The unit circle is an integral part to helping you succeed in trigonometry. Memorize every part of it (it’s not as overwhelming as it would appear at first glance), and use it to your advantage. During my college trigonometry class, I drew the unit circle on the back of every single one of my tests before getting started.
Helpful Tips
The angles 0, 90, 180, and 270 should hopefully be obvious reference points for you. From these angles, you are going to add 30 degrees to get to the next angle, then you are going to add 15 until you get to the next quadrantal angle.
There are only three main coordinates that you have to memorize. They stay in the same order on each side if you start from the x-axis. The only thing that changes is their sign depending on what quadrant they are in.
Remember that x and y are positive in quadrant 1, x is negative and y is positive in quadrant 2, both x and y are negative in quadrant 3, and x is positive and y is negative in quadrant 4.
**Cosine is equal to the x and sine is equal to the y ALWAYS. I.E. (cos, sin).
Let’s spell it out:
\text{sin}\theta = \text{y} \ \ \ \ \ \ \ \ \ \ \text{csc}\theta = \frac{1}{\text{y}}\\ \text{cos}\theta = x \ \ \ \ \ \ \ \ \ \ \text{sec}\theta = \frac{1}{\text{x}} \\ \text{tan}\theta = \frac{\text{y}}{\text{x}} \ \ \ \ \ \ \ \ \ \ \text{cot}\theta = \frac{\text{x}}{\text{y}}Practice writing out the unit circle until you are comfortable with it and have it memorized. Keep this in your back pocket as it will most definitely save you time and come in handy.