Page 132 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, College Preparation
1. determine the values of the trigonometric ratios for angles less than 360o, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
2. make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
3. demonstrate an understanding that sinusoidal functions can be used to model some periodic phenomena, and solve related problems, including those arising from real-world applications.
1. Applying Trigonometric Ratios
2. Connecting Graphs and Equations of Sinusoidal Functions
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
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C. TRIGONOMETRIC FUNCTIONS OVERALL EXPECTATIONS
By the end of this course, students will:
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 determine the exact values of the sine, cosine, and tangent of the special angles 0°, 30°, 45°, 60°, 90°, and their multiples
1.2 determine the values of the sine, cosine, and tangent of angles from 0o to 360o, through investigation using a variety of tools (e.g., dynamic geometry software, graphing tools) and strategies (e.g., applying the unit circle; examining angles related to the special angles)
1.3 determine the measures of two angles from 0o to 360o for which the value of a given trigono- metric ratio is the same (e.g., determine one angle using a calculator and infer the other angle)
Sample problem: Determine the approximate measures of the angles from 0o to 360o for which the sine is 0.3423.
1.4 solve multi-step problems in two and three dimensions, including those that arise from real-world applications (e.g., surveying, navi-
gation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios
Sample problem: Explain how you could find the height of an inaccessible antenna on top of a tall building, using a measuring tape, a clinometer, and trigonometry. What would you measure, and how would you use the data to calculate the height of the antenna?
1.5 solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law (including the ambiguous case) and the cosine law
Sample problem: The following diagram represents a mechanism in which point B is fixed, point C is a pivot, and a slider A can move horizontally as angle B changes. The minimum value of angle B is 35o. How far is it from the extreme left position to the extreme right position of slider A?
28 cm
20 cm
A
C
By the end of this course, students will:
2.1 make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the rela- tionship between angles from 0o to 360o and the corresponding sine ratios or cosine ratios, with or without technology (e.g., by genera- ting a table of values using a calculator;
by unwrapping the unit circle), defining this relationship as the function f (x) = sin x or f (x) = cos x, and explaining why the rela- tionship is a function