K. Stewart
MHF4U Unit Outline
Chapter 4: Trigonometry
Did you know that scientists, engineers, designers and other professionals who use angles in their daily work generally do
not measure the angles in degrees? In this chapter, you will investigate using radian measure instead of degree
measure. You will extend the use of radian measure to trigonometric ratios to see the advantages of using radian
measure. You will extend your work in grade 11 with trigonometry to develop trig formulas for compound angles. You will
investigate equivalent trig expressions using a variety of approaches and you will identify and prove trig identities using a
variety of techniques.
By the end of this chapter, you will be assessed on your ability to:
B1.0
B3.0
demonstrate an understanding of the meaning and application of radian measure;
…prove trigonometric identities.
Section
4.1 Radian
Measure
(two days)
Learning goals
Rides that spin – is it better to be on the
inside or the outside?
How do gears work and what does size have
to do with it?
Vocab: radius, radii, radian, rad, pi,
circumference, arc, arc length, sector,
central angle, subtends, theta, ratio, angular
velocity
Key equation:

a
r
Homework
Day 1:
Pg 200 #1 – 14 (last part of each) mandatory
Use the Prerequisite Skills Appendix (page 484) for a mini
lesson on any concept not understood (sections are in
alphabetical order)
Day 2:
Check for understanding of prerequisite skills
Pg 208 #1 – 8, 10, 15, 16 optional
Pg 208 # 2d, 4d, 6f, 7f, 8f, 9, 11, 13, 17, 18
mandatory
Skills: describing meanings and purpose of positive and
negative trig ratios, comparing the two meanings inverse
with respect to trig functions, being able to calculate inverse
ratios, identifying number of radians in a circle, memorizing
special angles (e.g. 30 o   , 45o   ), converting between
6
4
degrees and radians both exact and approximate, solving
problems involving arc length, solving rate of change
problems involving things that spin or revolve.
4.2 Trigonometric
Ratios and
Special Angles
How can we use special angles to determine
exact measurements in our designs?
Vocab: special angles, unit circle, terminal
arm, standard position, primary trig ratios
[sine (sin), cosine (cos), tangent (tan)],
reciprocal trig ratios [cosecant (csc), secant
(sec), cotangent (cot)], CAST rule
Pg 216 #1 – 8, 11, 16, 17, 18 optional
Pg 217 # 9, 10, 12, 13, 19 mandatory
4.3 Equivalent
Trigonometric
Expressions
(two days)
What other angles can we figure out from
the ones we know so that we can be
exact?
Vocab: equivalent trig expressions, identity,
trig identity, cofunction identities (also
known as correlated angle identities),
congruent
Notation: P’ (read ‘P prime’) is the
transformation of P;  ”means congruent to”
Pg 225 #1, 3, 5, 7, 9 optional
Pg 225 # 2, 4, 6, 8, 10, 12 mandatory (first day)
Pg 226 #11, 14, (one of 15 to 19), 20 (one
verification), 21, 22
Skills: Using trig ratios to solve problem involving angles,
use special angles to get exact solutions, use the CAST rule
to determine exact values for the trig ratios of multiples of
the special angles, explain what the trig ratios are and what
they mean.
Skills: Use a right triangle or unit circle to derive equivalent
trig expressions, using equivalent trig expressions to simplify
other expressions or to evaluate other expressions, using
graphing technology to verify equivalent trig expressions
(continued next page)
K. Stewart
4.4 Compound
Angle Formulas
4.5 Prove
Trigonometric
Identities
What other angles can we figure out from
the ones we know so that we can be
exact?
Vocab: compound angle expression, compound
angle formula, double angle formulas
Pg 232 #1 – 9, 12, 18 optional
Pg 233 # 10, 11bd, 13, 14b, 15ab, 17 mandatory
Prove it!
Vocab: counterexample,
Basic trig identities are: Pythagorean identity,
quotient identity, reciprocal identities and
compound angle formulas
Pg 240 #1 – 8, 11, 13, 15 optional
Pg 241 # 9, 10, 12, 16, 17, 18 mandatory
Skills: verify/test compound angle formulas, determine exact
trig ratios for angles other than special angles, develop
compound angle formulas using algebra and the unit circle,
use equivalent trig expressions to develop new compound
angle formuolas from existing compound angle formulas,
apply compound angle formulas to determine exact trig ratios
for angles that can be expressed as sums or differences of
special angles, use counter examples to show that something
is not generally true.
Skills: using identities and formulas to prove other identities
or formulas (e.g. use a compound angle formula to prove a
double angle formula or cofunction identity), use graphing to
to investigate an identity, use substitution of equivalent trig
expressions to prove identities, use trig identities to simplify
solutions to problems that result in trig expressions.
The Chapter will wrap up with a review and a summative. Class discussions, class work, homework and quizzes will help
you to determine how well you understand the course material in preparation for the summative assessments.
Extra help is available every day period 2, 5 and after school!