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MHF4U: Advanced Functions, Grade 12

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  1. Course Outline
    Course Outline
  2. Unit 1
    Lesson 1 - Introduction To Logarithms
    1 Quiz
  3. Lesson 2 - Solving Logarithms
    1 Quiz
  4. Lesson 3 - Laws of Logarithms
    1 Quiz
  5. Lesson 4 - Real World Applications of Logarithms
    1 Quiz
  6. UNIT 2
    Lesson 5 - Understanding Radian Measure
    1 Quiz
  7. Lesson 6 - Primary Trigonometric Ratios
    1 Quiz
  8. Lesson 7 - Reciprocal Trigonometric Ratios
    1 Quiz
  9. Lesson 8 - Trigonometric Function Values of Special Angles
    1 Quiz
  10. Lesson 9 - Graphing the Sine and Cosine Functions
    1 Quiz
  11. Lesson 10 - Graphing the Tangent Functions
    1 Quiz
  12. UNIT 3
    Lesson 11 - Vertical Displacement, Amplitude and Phase Shift
    1 Quiz
  13. Lesson 12 - Period of a Function
    1 Quiz
  14. Lesson 13 - Trigonometric Identities (Pythagorean, Reciprocal and Quotient Identities)
    1 Quiz
  15. Lesson 14 - Polynomial Functions
    1 Quiz
  16. Lesson 15 - Dividing Polynomials by a Polynomial
    1 Quiz
  17. UNIT 4
    Lesson 16 - The Remainder Theorem
    1 Quiz
  18. Lesson 17 - Factor Theorem
    1 Quiz
  19. Lesson 18 - Solving Polynomials: Factoring
    1 Quiz
  20. Lesson 19 - Solving Polynomial Inequalities
    1 Quiz
  21. Lesson 20 - Average and Instantaneous Rate of Change
    1 Quiz
Lesson 22 of 21
In Progress

Lesson 9 – Graphs of the Primary Trigonometric Functions

Learning Goals:

  • Use radians to graph the primary trigonometric functions.

The Unit Circle

The unit circle is a circle that is centered at the origin and has a radius of 1 unit. On the unit circle, the sine and cosine functions take a particularly simple form:

The value of  is the y-coordinate of each point on the circle , and the value of is the x-coordinate. As a result, each point on the circle can be represented by the ordered pair:

(x, y) = ()

Where  is the angle formed between the positive x-axis and the terminal arm of the angle that passes through each point.

For example the point  lies on the terminal arm of the angle .

Evaluating each trigonometric expression using the special triangles results in the ordered pair .

Repeating this process for other angles between 0 and 2π results in the following diagram:

Success Criteria:

I am able to

  • Use radians to graph the primary trigonometric functions.