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SolidWorks Lesson Template for Teachers to Contribute

Cover Sheet for Exemplary Lessons/Units Project

Faculty Member Name: Melody Thomas Date: August 26, 2006

School District: Shelby County Schools

Teacher’s School email address: [email protected]

Title of Lesson/Unit: Exploring Trigonometric Ratios

Applicable for Algebra 2, Advanced Math and PreCalculus

Science, Technology, Engineering and Math) STEM Concepts Addressed: This lesson allows students to examine trigonometric ratios on circles of varying radii, thereby discovering that these ratios remain constant regardless of the radius of the circle. Students will then construct a circle of radius 1 and compare the trigonometric ratios found earlier with the x and y coordinates of the point of intersection of the radius and circumference of the circle.

Length of instruction period: 55 minutes

How many periods needed to implement lesson unit: 1

Grade Level(s) for use: 10 th , 11 th and 12 th

Objectives: 1. Calculate trigonometric ratios for circles of various sizes at designated angle measures.

2. Compare the calculated ratio with x and y coordinates on a unit circle at designated angle measures.

3. Create a plan to determine trigonometric values for any angle.

Materials: SolidWorks, Trigonometric Ratio Worksheet, Calculator, Pencil

Procedures: 1. Construct a circle on the Front Plane, record the radius of the circle on the worksheet. 2. Sketch a horizontal line to represent the x axis 3. Sketch a vertical line to represent the y axis 4. Sketch a diagonal line starting at the origin and ending on the circumference of the circle in quadrant 1. 5. Dimension the angle, adjust the measure to a multiple of 10. 6. Find the horizontal dimension from the origin to the end of the diagonal line, record this measure on the worksheet. 7. Find the vertical dimension from the origin to the end of the diagonal line, record this measure on the worksheet. 8. Dimension the diagonal line to find the length, record this measure on the worksheet. 9. Repeat steps 1 – 8 twice, each time using a different radius. 10. Construct a circle with radius of 1. 11. Repeat steps 2 – 7. Assessment: Students will complete the attached worksheet by constructing three circles of varying size and recording horizontal/vertical/diagonal dimensions for each 10 degree angle in quadrant I. Students will then compare these measurements with the x and y coordinates of the points of intersection of each of these diagonals with the circumference of the unit circle.

Resources Used: N/A

Copyrighted Materials: N/A Trigonometric Ratio Worksheet

Record the measurements from the SolidWorks exercise in the following tables.

Circle 1: Radius ______

Cosine Ratio Sine Ratio Angle Horizontal Vertical Diagonal Horizontal/Diagonal Vertical/Diagonal 10 20 Circle 2: Radius  30 ______40 50 C S 60 o i 70 s n i e 80 n 90 e R R a a t t i i o o V H e o r r t i i AH V D z c no e i o a n l t / a D l i / a D g i o a n g a o l n a l 1 20 30 40 50 60 70 80 90 0 Circle 3: Radius ______

Cosine Ratio Sine Ratio Angle Horizontal Vertical Diagonal Horizontal/Diagonal Vertical/Diagonal 10 20 30 40 50 60 70 80 90

What do you notice about the values in the ratio columns? ______

______

Unit Circle:

Angle Horizontal Vertical 10 20 30 40 50 60 70 80 90

Do you recognize the values in this chart? ______

Summarize your findings: ______

______

Note any other patterns present in the Unit Circle table: ______

______

How could you use this information to find the value of sine and cosine for any angle? ____

______