Page 91 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

B. TRIGONOMETRIC FUNCTIONS OVERALL EXPECTATIONS
By the end of this course, students will:
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure
1.2 represent radian measure in terms of π (e.g.,
π radians, 2π radians) and as a rational number 3
(e.g., 1.05 radians, 6.28 radians)
1.3 determine, with technology, the primary trigonometric ratios (i.e., sine, cosine, tangent) and the reciprocal trigonometric ratios (i.e., cosecant, secant, cotangent) of angles expressed in radian measure
1.4 determine, without technology, the exact values of the primary trigonometric ratios and the reciprocal trigonometric ratios for
the special angles 0, π6 , π4 , π3 , π2 , and their multiples less than or equal to 2π
By the end of this course, students will:
2.1 sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in radians, and determine and describe some key properties (e.g., period of 2π, amplitude of 1) in terms of radians
2.2 make connections between the tangent ratio and the tangent function by using technology to graph the relationship between angles in radians and their tangent ratios and defining this relationship as the function f(x) = tan x, and describe key properties of the tangent function
2.3 graph, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions (i.e., cosecant, secant, cotangent) for angle measures expressed in radians, determine and describe key proper- ties of the reciprocal functions (e.g., state the domain, range, and period, and identify and explain the occurrence of asymptotes), and recognize notations used to represent the reciprocal functions [e.g., the reciprocal of
f(x) = sin x can be represented using csc x,
1 ,or 1 ,butnotusingf–1(x)orsin–1x, f(x) sinx
which represent the inverse function]
TRIGONOMETRIC FUNCTIONS
1. demonstrate an understanding of the meaning and application of radian measure;
2. make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;
3. solve problems involving trigonometric equations and prove trigonometric identities.
1. Understanding and Applying Radian Measure
2. Connecting Graphs and Equations of Trigonometric Functions
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Advanced Functions
MHF4U