Problem Solving and Discussion to Discover Trigonometry Aviva

Problem Solving and Discussion to Discover Trigonometry Aviva Halani Phillips Exeter Academy ahalani@exeter. edu All problems available here: https: //www. exeter. edu/mathproblems

Mathematics at Phillips Exeter �Discussion-based instruction �Students present solutions �Instructors guide conversation �Problem-based curriculum �Integrated topics �Algebra, geometry, trigonometry woven together �Calculus, Statistics, Discrete Topics, Linear Algebra, … �Spiraling materials �Ideas built up through Math 1, Math 2, Math 3, and Math 4 All problems available here: https: //www. exeter. edu/mathproblems

Example Pages from Math 3 -4 All problems available here: https: //www. exeter. edu/mathproblems

Looking at Math 2 All problems available here: https: //www. exeter. edu/mathproblems

Slopes and angles between lines All problems available here: https: //www. exeter. edu/mathproblems

Let’s try some Math 3 -4 problems Put yourselves in the shoes of students who only know right-triangle trigonometry. Try these two problems: All problems available here: https: //www. exeter. edu/mathproblems

More problems building to Law of Cosines All problems available here: https: //www. exeter. edu/mathproblems

Let’s generalize All problems available here: https: //www. exeter. edu/mathproblems

Building up to Law of Sines All problems available here: https: //www. exeter. edu/mathproblems

Sum Formulas All problems available here: https: //www. exeter. edu/mathproblems

Sum Formulas using Matrices All problems available here: https: //www. exeter. edu/mathproblems

Sum Formulas using Matrices All problems available here: https: //www. exeter. edu/mathproblems

Ferris Wheel All problems available here: https: //www. exeter. edu/mathproblems

Cycloid All problems available here: https: //www. exeter. edu/mathproblems

Cycloid All problems available here: https: //www. exeter. edu/mathproblems

Cycloid All problems available here: https: //www. exeter. edu/mathproblems

Ellipses All problems available here: https: //www. exeter. edu/mathproblems

Coordinates in 3 dimensions All problems available here: https: //www. exeter. edu/mathproblems

Thank you! All problems available here: https: //www. exeter. edu/mathproblems Additional resources available via email: ahalani@exeter. edu Want more? We have summer conferences: https: //www. exeter. edu/programs-educators All problems available here: https: //www. exeter. edu/mathproblems