Page 67 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

C. TRIGONOMETRIC FUNCTIONS OVERALL EXPECTATIONS
By the end of this course, students will:
1. solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications;
2. demonstrate an understanding of periodic relationships and the sine function, and make connections between the numeric, graphical, and algebraic representations of sine functions;
3. identify and represent sine functions, and solve problems involving sine functions, including problems arising from real-world applications.
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 solve problems, including those that arise from real-world applications (e.g., surveying, navigation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios
1.2 solve problems involving two right triangles in two dimensions
Sample problem: A helicopter hovers 500 m above a long straight road. Ahead of the heli- copter on the road are two trucks. The angles of depression of the two trucks from the helicopter are 60° and 20°. How far apart are the two trucks?
1.3 verify, through investigation using technol- ogy (e.g., dynamic geometry software, spreadsheet), the sine law and the cosine law (e.g., compare, using dynamic geometry
software, the ratios a , b , and c sinA sinB sinC
in triangle ABC while dragging one of the vertices)
1.4 describe conditions that guide when it is appropriate to use the sine law or the cosine law, and use these laws to calculate sides and angles in acute triangles
1.5 solve problems that require the use of the sine law or the cosine law in acute triangles, including problems arising from real-world applications (e.g., surveying, navigation, building construction)
By the end of this course, students will:
2.1 describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications (e.g., natural gas consumption in Ontario, tides in the Bay of Fundy), given a numeric or graphical representation
2.2 predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function (e.g., predicting hours of daylight on a particular date from previous measure- ments; predicting natural gas consumption in Ontario from previous consumption)
2.3 make connections between the sine ratio and the sine function by graphing the relationship between angles from 0o to 360o and the corresponding sine ratios, with or without technology (e.g., by generating a table of values using a calculator; by unwrapping the unit circle), defining this relationship as the function f(x) = sinx, and explaining why the relationship is a function
TRIGONOMETRIC FUNCTIONS
1. Applying the Sine Law and the Cosine Law in Acute Triangles
2. Connecting Graphs and Equations of Sine Functions
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Functions and Applications
MCF3M