Alberta Program of Studies (2002)

Topic 3: Trigonometry

General Outcome: Solve exponential, logarithmic and trigonometric equations and identities.

Substrand: Variables and Equations

Specific Outcomes

3.1 Distinguish between degree and radian measure, and solve problems using both. [CN, E]

3.2 Determine the exact and the approximate values of trigonometric ratios for any multiples of 0°, 30°, 45°, 60° and 90° and 0, π/6, π/4, π/3, π/2 [CN, E]

3.3 Solve first and second degree trigonometric equations over the domain 0 ≤ θ < 2π or 0° ≤ θ < 360°

• algebraically
• graphically.
  [PS, T]

3.4 Determine the general solutions to trigonometric equations where the domain is the set of real numbers. [PS, T]

3.5 Verify trigonometric identities:

• numerically for any particular case
• algebraically for general cases
• graphically.
  [PS, R, T, V]

General Outcome: Represent and analyze trigonometric functions, using technology as appropriate.

Substrand: Relations and Functions

Specific Outcomes:

3.6 Describe sine, cosine and tangent as circular functions, with reference to the unit circle and an angle in standard position. [PS, R, V]

3.7 Use sum, difference and double angle identities for sine and cosine to verify and simplify trigonometric expressions. [R, T]

3.8 Draw (using technology), sketch and analyze the graphs of sine, cosine and tangent functions, for:

• amplitude, if defined
• period
• domain and range
• asymptotes, if any
• behaviour under transformations.
  [CN, T, V]

3.9 Draw and sketch (using technology) and analyze the graphs of secant, cosecant and cotangent functions, for:

• period
• domain and range
• symptotes
• behaviour under horizontal and vertical stretches. [CN, T, V]

  Note: Transformations of secant, cosecant and cotangent graphs have been restricted to horizontal and vertical stretches.

3.10 Use sine and cosine functions to model and solve problems. [PS, R, V]

Note: Trigonometric modelling of real-life contexts has been restricted to the use of sine and cosine functions.

• Communication [C]
• Connections [CN]
• Estimation and Mental Mathematics [E]
• Problem Solving [PS]
• Reasoning [R]
• Technology [T]
• Visualization [V]