Pre-calculus can be the first hard math class for some people. The information not as straight forward as other math, and getting good grades is a challenge. One of the hardest parts of pre-calculus is the trigonometry unit. The trigonometry learned in pre-calc is essential to move on to calculus, specifically the unit circle. Many people find it difficult to memorize, which is why I have compiled a list of tips and tricks to assist anyone who is having trouble memorizing it.

TIP 1: There is more logic to the unit circle than you might think. For example when asked to find the forty-five degree measure on the unit circle there is actually a mathematical way to find the answer. All you have to do is draw a line from the origin, to the point of the circle you are trying to find. You will know the inside angle in our example problem so you can label it. You also know that one of the angles that drops from the unknown point down to the x-axis is 90 degrees. So all you have to do is know how to find the regular sides of a 45 45 90 triangle, and then apply it to find the distances from the origin to the point along the x-axis, which will be the cosine value, and then solve for the values that go up, the sine values. If you can do this, then the rest of the unit circle should be a breeze.

TIP 2: This tip is a little simpler. All you have to do is know the 5 values that make up the unit circle: 0, sqrt(2)/2, ½, and sqrt(3)/2 and 1. Now just remember that when ever the angle is 45, 135, 215, or 305 the point will always be (sqrt(2)/2, sqrt(2)/2). This is actually quite easy to get the hang of if you use 45 as a reference. Now for the 30 and 60 degree angles and their multiples you use a similar technique. All you have to do is eyeball the distance from the origin up and down. If it goes over a lot, then you use sqrt(3)/2, and if it goes over a little then use ½. This can also be repeated for the y-values. Its that easy!