2018 Grade 11 Enriched Outline (MCR3U6)

# Unit 3:Trigonometry

Pink topics are pure enrichment topics

Yellow topics are 11U topics, with more difficulty or rigor

Blue topics are 12U material required for MHF4U

## Homework

18

Intro for Unit 3 – Trigonometry

Solving Triangles

Proving Sine Law

Proving Cosine Law

Triangle Inequality

3D Trigonometry

Optional Quiz – Logarithms (no calculators)

Proving Sine Law and Cosine Law

• You can use the blank handout above, or use your own paper
• You can check here for HINTS
• You can check here for a full proof.

Handout, 3D Trig Problems #4, 6, 7, 13

Triangle Inequality (Check here for solutions.)

1.9 P81 Achievement Check  (Check here for solutions.)

4.1 P275 #19

4.3 P291 #8—11

4.3 P294 Achievement Check

19

Test 2 – Functions

22

PA Day

23 Ont College Fair

Sine Law, The Ambiguous Case

4.4 P308 #1—9 (odd letters)

24 Ont College Fair

Sine Law, The Ambiguous Case II

4.4 P310 #10—19

4.4 P311 Achievement Check

25 Parent’s Night

Optional Lessons (using the CEMC site for MHF4U):

• 6.1  Lessons 1 & 2 only – Radians explained; converting between radians and degrees
• 6.2  The Unit Circle – watch all lessons 1 to 4

Notes:

Homework:

5.1 P334 #1—9 (odd), 11, 17, 18, 19, 20, 22, 24, 28 (r/min means “revolutions per min”)

26

The Ambiguous Case III – Cosine Law vs. Sine Law

5.2 Trig Ratios of Any Angles

Evaluating Trig Exactly

Memorizing special angles

Co-terminal Angles

The Terminal Angle where

Special angles 30˚, 45˚, 60˚.

CAST memory aid (it’s not a rule)

Handout, Evaluating Trig Exactly

5.2 P348 #5—11, 18

Optional Lessons (using the CEMC site for MHF4U):

• 6.3  Trigonometric Ratios and Special Triangles

Optional: Investigate Cosine Law and The Ambiguous Case, P312 #1—4

29

Unwrapping the Unit Circle (protractors, no calculators!)

5.5 Stretches of Periodic Functions

Handout, Unwrapping the Unit Circle

Handout, Graphing Trig Functions

5.5 P374 #1—12 (odd)

Check out the Transformations of Sine using Desmos

30

5.3 Modelling Periodic Behaviour

5.6 Transformations of Trigonometric Functions

Quiz – trigonometry (no calculator)

5.3 P359 #1, 2, 4

5.6 P387 #1—10 (odd)

Get the handout, Applications of Periodic Functions from Mr. Shim, but it is for tomorrow’s homework.

31

Graphs of Reciprocal Trigonometric Functions

Applications of Sinusoidal Functions

Test 2 Corrections due

In class:

·         Handout, The Reciprocal Functions (check here for answers, or use graphing software.)

·         Handout, Sinusoidal Regression

Homework:

• Handout, Applications of Periodic Functions  (check here for page 5, the answers)

5.5 P377 #17—19

5.6 P388 #12—18, 21

Nov 1st

Introduction to Trig Identities

Quiz – Graphing Trig Functions

Trigonometric Identities P1—3 examples only  (check answers here)

Optional 5.7 P398 #2, 3

5.7 P398 #4odd , 7odd, 8, 11, 18, 20 (view an example of #20)

2

Trig Identities II

Trigonometric Identities P4 #1—14

5 staff mtg

Trig Identities III

Hand in Learning Skills sheet

Trigonometric Identities (the rest) P4 #15—28

6 Diwali

Solving Trig Equations

5.8 P408#1—6(odd), 10—12

7

Solving Trig Equations II

5.8 P409 #7—9, 13—15 (14 & 15 in radians and exact)

8

Solving Trig Equations III

Solving Trig Equations (just 2 questions.)

9 Remembrance Day

Assembly Timetable:

Period 1 8:50—10:50

Period 2 10:55—12:00

Period 3 12:05—1:10

Period 4 1:15—2:20

Period 5 2:25—3:30

P313 Ch. 4 Review Trigonometry

P412 Ch. 5 Review Trigonometric Functions

Optional:

Watch the lessons on the CEMC Advanced Functions website for Compound Angle Formulas.

12

Trig Identities IV – 7.3 Compound Angle Formulas

Do the exercises on the CEMC Advanced Functions website for Compound Angle Formulas.

Watch the lessons on the CEMC Advanced Functions website for Double Angle Formulas.

13

Trig Identities V – 7.4 Double Angle Formulas

Do the exercises on the CEMC Advanced Functions website for Double Angle Formulas.

Watch the lessons on the CEMC Advanced Functions website for Solving Trigonometric Equations.

14 Take your kids to work day; Gr 8 orientation

7.5 Solving Trigonometric Equations

Do the exercises on the CEMC Advanced Functions website for Solving Trigonometric Equations.

15

Polar Coordinates

Plotting polar coordinates

Converting between Cartesian and polar coordinates

Polar Curves

Graphing polar functions with a table of values (manually)

Graphing polar functions using software (Graph; Geometer Sketchpad; Desmos)

Handout, Polar Coordinates  (Check completed notes here.)

Handout, Polar Curves (Check completed notes here.)

16

Test 3

19

Polar Curves II

Complete previous homework graphing manually; check with others

Using software to graph

Handout, Polar Curves II

Use Desmos to graph polar functions.

20 Report cards

Complex Numbers in Polar Form

DeMoivre’s Theorem – powers of complex numbers

DeMoivre’s Theorem II – roots of complex numbers

Handout, Complex Numbers in Polar Form (check your completed notes here.)

Do #1, 2, 5—7

Review proofs for #3 and #4 here.

DeMoivre’s Theorem  (Check your completed notes here.)

DeMoivre’s Theorem II  (Check your completed notes here.)

Optional: (for computer programmers)

Khan Academy has a nice lesson using Polar Coordinates when programming the shape of a circular path on the screen.  “Not so easy,” in Cartesian, but simple in Polar form.  Enjoy.