What is 60 ° 60\degree 6 0 ° in radians?

π 3 r a d i a n s \frac{\pi}{3}\ radians 3 π r a d i a n s

3 π 4 r a d i a n s \frac{3\pi}{4}radians 4 3 π r a d i a n s

What is the correct ordered pair for an angle rotation of 150 ° 150\degree 1 5 0 ° ?

( − 3 2 , 1 2 ) \left(\frac{-\sqrt{3}}{2},\ \frac{1}{2}\right) ( 2 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 2 1 )

( 3 2 , 1 2 ) \left(\frac{\sqrt{3}}{2},\frac{1}{2}\right) ( 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 2 1 )

( − 3 2 , − 1 2 ) \left(\frac{-\sqrt{3}}{2},\frac{-1}{2}\right) ( 2 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 2 − 1 )

( 3 2 , − 1 2 ) \left(\frac{\sqrt{3}}{2},\frac{-1}{2}\right) ( 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 2 − 1 )

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

( 1 2 , − 3 2 ) \left(\frac{1}{2},\ \frac{-\sqrt{3}}{2}\right) ( 2 1 , 2 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

( 1 2 , 3 2 ) \left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right) ( 2 1 , 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

( − 1 2 , 3 2 ) \left(\frac{-1}{2},\ \frac{\sqrt{3}}{2}\right) ( 2 − 1 , 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

( − 1 2 , − 3 2 ) \left(\frac{-1}{2},\ \frac{-\sqrt{3}}{2}\right) ( 2 − 1 , 2 − 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

Introduction To The Unit Circle

Introduction to the Unit Circle

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.TF.A.2, HSF.TF.A.1

Standards-aligned

Melanie Buch

Used 26+ times

FREE Resource

3 Slides • 6 Questions

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.

Introduction to the Unit Circle

Algebra 2 Unit 11

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