Unit Circle: Memorizing the First Quadrant

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  • 0:06 Memorizing the First Quadrant
  • 2:27 First Quadrant Points
  • 3:51 SIN, COS, and TAN of…
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Lesson Transcript
Instructor: Tyler Cantway

Tyler has tutored math at two universities and has a master's degree in engineering.

Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.

Memorizing the First Quadrant

Some of the more useful study skills you can learn are actually memorization tricks to make complicated information simpler. When it comes to math, sure, there are things you just have to remember. These can be things like basic addition and subtraction all the way up to trig functions.

But there are some things in math where it's more helpful to remember a few short patterns rather than try to memorize everything. For trigonometric calculations, the most important thing you can memorize is the unit circle. The unit circle contains several useful angles along with their x and y coordinates.

Memorizing the unit circle can be extremely helpful because, if you have it memorized, you can calculate the trig values of the angles without a calculator. You can even go backwards by taking a trig value and finding the angle that created it. Now, you may be worried that memorizing this will be impossible. Don't worry. There are a few patterns that we can learn to make it a lot easier and more useful.

First Quadrant Angles

Even though the unit circle has four quadrants, most of them are just small twists on the first quadrant. Believe it or not, there are a few patterns in the first quadrant to help us memorize it.

The first quadrant angles range from zero degrees to 90 degrees. To get angles in between, we split it in half and in thirds. This gives us angles of zero, 30, 45, 60, and 90 degrees. Now that we know the degree measures for the angles, we need to write the radian measures. You can convert all the degree measures into radian measures by multiplying them by 2pi/360.

Let's do this for zero and 90 degrees. Zero multiplied by anything is zero, so that angle is zero radians. 90*2pi/360 simplifies to pi/2 radians. For the other three angles, you can convert or you can use a pattern. Take the first number from the angle in degrees and put pi over them. Reverse the order and you have pi/6, pi/4, and pi/3.

First Quadrant Points

Knowing the angles is the first step, but to be able to do calculations, we have to know the x and y coordinates for each angle. Again, we will start with the zero and 90 degree angles. These are straightforward. The coordinates are read directly off the graph. The point for a zero angle on the unit circle is the point (1,0). The point for a 90 degree or pi/2 radian angle is the point (0,1).

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