Download f_tf_a_1_task_building_the_unit_circle

HCPSS Worthwhile Math Task
Building the Unit Circle
Common Core Standard
F.TF.A.1 Understand radian measure of an angle as the length of an arc on the unit circle
subtended by the angle.
MP1:
MP2:
MP3:
MP4:
MP5:
MP6:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Algebra II, Unit 7
The Task
1. Using your knowledge of the special triangle and trigonometric ratios, find the exact value of
the missing sides for each triangle below.
1
1
1
30º
45º
60º
2. Now, arrange these triangles in the appropriate position in the first quadrant of the circle on
page one. Be certain to anchor the labeled angle at the origin and the base along the x-axis. Label
the point where each triangle intersects the circle A, B and C.
3. Evaluate the sine and cosine of the labeled angles using the length of the sides of the
special triangles. Be certain to rationalize the denominator for each ratio.
4. Find the coordinates of points A, B, and C using the values from #3.
5. Use this information to find the corresponding coordinates in the remaining quadrants.
6. Now, fill-in all blank coordinates on page three along with corresponding angles in radians
and degrees.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Image from page one
Image from page two
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(0,0)
r=1
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Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
(___,___ )
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Facilitator Notes
1. This task follows the lesson seed F.TF.A.1 radian measures of angle and arc.
2. Prior to this task, assess students’ prior knowledge of special right triangles and similar
triangles. If needed, have students review the video
(https://www.youtube.com/watch?v=lVp5g2esbe4) to revisit the prerequisite skills. Make
this video available throughout the task.
3. Assign students to groups of 3-4. Introduce the task and monitor the conversation around
the processes that students use to complete the task.
Follow-Up Questions
1. What were some methods that your group used to find the coordinates in the remaining
quadrants? (If it appears that students used similar methods, solicit the class for possible
alternative methods.)
2. Identify some of the patterns you notice in the unit circle.
Solutions
http://www.gradeamathhelp.com/unit-circle.html
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.