Question

How do you memorize a unit circle ?

Answer 1

Hint:You can memorize a unit circle by seeing the x-axis or y-axis , you can memorize it by x-axis by seeing that the x-axis is not a fraction , we have to think x-axis as a whole number. You can memorize it by y-axis by seeing that the y-axis has a denominator that is two, we have to think of the y-axis as a fraction number.

Complete answer:
Method I: See that the x-axis is not a fraction. It’s helpful to consider your x-axis as an entire number. The positive side is $0$ or $2\pi $, while the negative side is $1\pi $. That is because the highest part of the circle by itself measures $1\pi $, plus the rock bottom, a part of the circle by itself also measures $1\pi $. The negative side of the x-axis is halfway around your circle, while the positive side is both the beginning and finish of the circle.

Method II:
Notice that the y-axis has a denominator of two. Since the whole top half, the circle measures $1\pi $, it is sensible that the measurement of the positive y-axis would be $\dfrac{{1\pi }}{2}$ . That’s because the y-axis splits the highest part of the circle in half. Similarly, the rock bottom part of the circle is $\dfrac{{3\pi }}{2}$ because the negative y-axis is splitting it in half.
• If you have trouble remembering that the negative y-axis is $\dfrac{{3\pi }}{2}$ , you can use the addition trick for finding the third quadrant radians.

Note:A unit circle features a radius (r) of one, which provides it a circumference of $2\pi $, since circumference is equal to $2\pi r$. The unit circle allows you to simply see the connection between cosine and sine coordinates of angles, also because the measurement of the angles in radians.