Mathematics

2.2 determine, through investigation using avariety of tools (e.g., calculators, dynamicgeometry software, manipulatives) and strategies(e.g., modelling; making a table of values;graphing), the optimal dimensions of a twodimensionalshape in metric or imperial unitsfor a given constraint (e.g., the dimensionsthat give the minimum perimeter for a givenarea)Sample problem: You are constructing a rectangulardeck against your house. You willuse 32 ft of railing and will leave a 4-ft gapin the railing for access to stairs. Determinethe dimensions that will maximize the areaof the deck.2.3 determine, through investigation using a varietyof tools and strategies (e.g., modelling withmanipulatives; making a table of values;graphing), the optimal dimensions of a rightrectangular prism, a right triangular prism,and a right cylinder in metric or imperial unitsfor a given constraint (e.g., the dimensionsthat give the maximum volume for a givensurface area)Sample problem: Use a table of values and agraph to investigate the dimensions of a rectangularprism, a triangular prism, and a3cylinder that each have a volume of 64 cmand the minimum surface area3. Solving Problems InvolvingTrigonometryBy the end of this course, students will:3.1 solve problems in two dimensions usingmetric or imperial measurements, includingproblems that arise from real-world applications(e.g., surveying, navigation, buildingconstruction), by determining the measuresof the sides and angles of right triangles usingthe primary trigonometric ratios, and of acutetriangles using the sine law and the cosine law3.2 make connections between primary trigonometricratios (i.e., sine, cosine, tangent) ofobtuse angles and of acute angles, throughinvestigation using a variety of tools andstrategies (e.g., using dynamic geometrysoftware to identify an obtuse angle withthe same sine as a given acute angle; usinga circular geoboard to compare congruenttriangles; using a scientific calculator to comparetrigonometric ratios for supplementaryangles)3.3 determine the values of the sine, cosine, andtangent of obtuse angles3.4 solve problems involving oblique triangles,including those that arise from real-worldapplications, using the sine law (in nonambiguouscases only) and the cosine law,and using metric or imperial unitsSample problem: A plumber must cut a pieceof pipe to fit from A to B. Determine thelength of the pipe.A8Pipe115°3.5 gather, interpret, and describe informationabout applications of trigonometry in occupations,and about college programs that explorethese applicationsSample problem: Prepare a presentation toshowcase an occupation that makes use oftrigonometry, to describe the education andtraining needed for the occupation, and tohighlight a particular use of trigonometryin the occupation.5BFoundations for College MathematicsMAP4CGEOMETRY AND TRIGONOMETRY143