Introduction to the Unit Circle

Introduction to the Unit Circle

Algebra 2 Unit 11

Unit Circle Facts

• The unit circle has a center at the origin (0, 0) and a radius of 1

• Each coordinate on the unit circle corresponds to the number of degrees (or radians) that the radius has rotated.

• Common angle rotations are multiples of  $30\degree$ ( $\frac{\pi}{6}$  ) and  $45\degree\ \left(\frac{\pi}{4}\right)$  

Using the unit circle

One skill you must have is to use the unit circle to identify ordered pairs for a given angle rotation.

Multiple Choice

What is  $60\degree$ in radians?

• 60 radians

•  $\frac{3\pi}{4}radians$  

•  $\frac{\pi}{3}\ radians$  

• 10800 radians

Multiple Choice

 $Convert\ \frac{7\pi}{6}\ radians\ into\$  degrees.

•  $130\degree$  

•  $210\degree$  

•  $260\degree$  

•  $320\degree$  

Multiple Choice

What is the correct ordered pair for an angle rotation of  $150\degree$  ?

•  $\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$  

•  $\left(\frac{-\sqrt{3}}{2},\ \frac{1}{2}\right)$  

•  $\left(\frac{-\sqrt{3}}{2},\frac{-1}{2}\right)$  

•  $\left(\frac{\sqrt{3}}{2},\frac{-1}{2}\right)$  

Multiple Choice

What is the correct ordered pair for an angle rotation of  $\frac{5\pi}{3}$  ?

•  $\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$  

•  $\left(\frac{-1}{2},\ \frac{\sqrt{3}}{2}\right)$  

•  $\left(\frac{-1}{2},\ \frac{-\sqrt{3}}{2}\right)$  

•  $\left(\frac{1}{2},\ \frac{-\sqrt{3}}{2}\right)$  

Multiple Choice

What is the sign of the x-coordinate in Quadrant 3?

• Positive

• Negative

Multiple Select

Check the quadrants in which the y-value of the ordered pair on the unit circle is negative.

• Q1

• Q2

• Q3

• Q4