Embedded Files
A working knowledge of the unit circle is essential to your success in Calculus. You need to know that every point on the circle is represented through the sine and cosine functions in the form (cos(x), sin(x)). Sin(x) is the height of the functions and cos(x) is how far left or right the point is. The graphs below are a visual representation of this.
The unit circle uses weird increments (30, 45, 60, 90, 120, 145, etc) because the unit circle has nice values every 30 or 45 degrees. The table below shows what you must know to have a working knowledge of trig.
The first 2 rows show all of the possible values of sine and cosine at the "nice" values. The first row shows that you just increment the value in the square root as you move to the right. The second row shows the values you have probably seen in unit circles and math textbooks.
The next 2 rows show that cosine starts at 1 and then goes down to 0 at pi/2, which should remind you of this part of the cosine graph:
The last 2 rows show that sine starts at 0 and then goes to 1 at pi/2, which should remind you of this part of the sine graph:
All of these ideas lead to the unit circle as shown below:
A Practice worksheet I made for this quiz
See this website for some great gifs showing the relationship between the unit circle and radians.
The wikipedia page on the unit circle is quite helpful.
This is a worksheet with some trig practice.
Khan Academy has some great unit circle practice as well.
Google Sites
Report abuse