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Maths Quest 10 for New South Wales 5.3 Pathway
Work Programs
Chapter 7
Trigonometry
Strand: Measurement
Substrands and outcomes:
Trigonometry
MS5.1.2 Applies trigonometry to solve problems (diagram given) including those involving angles of elevation
and depression
MS5.2.3 Applies trigonometry to solve problems including those involving bearings
MS5.3.2 Applies trigonometric relationships, sine rule, cosine rule and area rule in problem solving
Section
Are you ready? (page 234)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD ROM)
SkillSHEETs (page 234)
7.1: Labelling right angled
triangles
7.2: Calculating sin, cos or
tan of an angle
7.4: Finding side lengths
in right-angled triangles
1
Technology applications
(CD ROM)
Learning outcomes
MS5.1.2
 identifying the
hypotenuse, adjacent and
opposite sides with
respect to a given angle
in a right-angled triangle
in any orientation
7.5: Calculating the angle
from the sin, cos or tan
ratio
7.6: Finding angles in
right-angled triangles
Trigonometry of rightangled triangles
(page 235)
WE 1, 2, 3, 4
Ex 7A Trigonometry of
right-angled triangles
(page 240)
Investigation:
Trigonometric identities
(page 242)
SkillSHEET 7.1: Labelling
right-angled triangles
(page 240)
SkillSHEET 7.2:
Calculating sin, cos or
tan of an angle
(page 240)
SkillSHEET 7.3:
Rearranging
trigonometric equations
(page 240)
SkillSHEET 7.4: Finding
side lengths in rightangled triangles
2
Mathcad: Triangle
(page 240)
Cabri geometry: SOH,
CAH, TOA (page 240)
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles to
find unknown sides
 using a calculator to find
an angle correct to the
nearest degree, given
one of the trigonometric
ratios of the angle
MS5.2.3
 using a calculator to find
approximations of the
trigonometric ratios of a
given angle measured in
degrees and minutes
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
MS5.1.2
 identifying the
hypotenuse, adjacent and
opposite sides with
respect to a given angle
in a right-angled triangle
in any orientation
 labelling the side lengths
of a right-angled triangle
in relation to a given
angle
 defining the sine, cosine
and tangent ratios for
angles in right-angled
(page 240)
SkillSHEET 7.5:
Calculating the angle
from the sin, cos or tan
ratio (page 240)
SkillSHEET 7.6: Finding
angles in right-angled
triangles (page 240)
SkillSHEET 7.7:
Composite shapes I
(page 241)
SkillSHEET 7.8:
Composite shapes II
(page 241)
Game time 001 (page 242)
3
triangles
 using trigonometric
notation
 using a calculator to find
approximations of the
trigonometric ratios of a
given angle measured in
degrees
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles to
find unknown sides,
including the hypotenuse
 labelling sides of rightangled triangles in
different orientations in
relation to a given angle
(Applying strategies,
Communicating)
 solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
MS5.2.3
 using a calculator to find
trigonometric ratios of a
given approximation for
angles measured in
degrees and minutes
 using a calculator to find
an approximation for an
angle in degrees and
minutes, given the
Applications of rightangled triangles
(page 242)
WE 5, 6a-b, 7, 8
Ex 7B Application of
right-angled triangles
(page 246)
Investigation: Fly like a
bird (page 248)
Code puzzle: (page 249)
Game time 002 (page 248)
4
Mathcad: SOH, CAH,
TOA (page 246)
Cabri geometry: Triangle
(page 246)
trigonometric ratio of the
angle
 finding unknown sides in
right-angled triangles
where the given angle is
measured in degrees and
minutes
 using trigonometric
ratios to find unknown
angles in degrees and
minutes in right-angled
triangles
 checking the
reasonableness of
answers to trigonometry
problems (Reasoning)
MS5.3.2
 determining and using
exact sine, cosine and
tangent ratios for angles
of 30°, 45° and 60°
MS5.1.2
 selecting and using
appropriate
trigonometric ratios in
right-angled triangles to
find unknown sides,
including the hypotenuse
 solving problems in
practical situations
involving right-angled
triangles (Applying
strategies)
MS5.2.3
 using three-figure
Non-right-angled triangles
– the sine rule
(page 250)
WE 9, 10, 11
Exercise 7C Non-rightangled triangles – the
sine rule (page 256)
WorkSHEET 7.1
(page 257)
5
Mathcad: Sine rule
(page 256)
bearings and compass
bearings
 drawing diagrams and
using them to solve word
problems which involve
bearings or angles of
elevation and depression
 solving simple problems
involving three figure
bearings (Applying
strategies,
Communicating)
 recognising directions
given as SSW, NE etc
(Communicating)
 interpreting directions
given as bearings
(Communicating)
 solving practical
problems involving
angles of elevation and
depression (Applying
strategies)
 checking the
reasonableness of
answers to trigonometry
problems (Reasoning)
MS5.3.2
 proving the sine rule
 using the sine rule to find
unknown sides and angles
of a triangle, including in
problems in which there
are two possible solutions
for an angle
Non-right angled-triangles
– the cosine rule
(page 258)
WE 12, 13, 14
Ex 7D Non-right angledtriangles – the cosine
rule (page 258)
10 Quick Questions 1
(page 262)
Area of triangles
(page 263)
WE 15, 16, 17
Ex 7E Area of triangles
(page 266)
Investigation: Which way
do I go? (page 268)
Maths Quest challenge
(page 268)
Mathcad: Cosine rule
(page 261)
WorkSHEET 7.2
(page 267)
6
Mathcad: Area of a
triangle (page 266)
 drawing diagrams and
using them to solve word
problems that involve
non-right-angled
triangles
 recognising that if given
two sides and an angle
(not included) then two
triangles may result,
leading to two solutions
when the sine rule is
applied (Reasoning,
Reflecting, Applying
strategies)
MS5.3.2
 proving the cosine rule
 using the cosine rule to
find unknown sides and
angles of a triangle
 drawing diagrams and
using them to solve word
problems that involve
non-right-angled
triangles
MS5.3.2
 proving and using the
area rule to find the area
of a triangle
 drawing diagrams and
using them to solve word
problems that involve
non-right-angled
triangles
 solving problems,
including practical
Circular functions
(page 269)
WE 18a-b, 19a-b
Ex 7F Circular functions
Investigation: The 4
quadrants of the unit
circle (page 270)
Identities (page 275)
WE 20a-b, 21, 22a-b
Ex 7G Identities
(page 277)
Investigation: Further
trigonometric identities
(page 278)
10 Quick Questions 2
(page 279)
Cabri geometry: Unit
circle (page 270)
Excel: Unit circle
(page 271)
Mathcad: Circular
functions (page 272)
GC program – Casio: Unit
circle (page 272)
GC program – TI: Unit
circle (page 272)
Cabri geometry: Unit
circle, sine and cosine
(page 272)
Cabri geometry: Unit
circle – tangent
(page 273)
WorkSHEET 7.3
(page 278)
7
problems, involving the
sine and cosine rules and
the area rule (Applying
strategies)
MS5.3.2
 establishing and using
the following
relationships for obtuse
angles, where
0  A  90 :
sin 180  A  sin A
cos180  A   cos A
tan 180  A   tan A
 finding the possible
acute and/or obtuse
angles, given a
trigonometric ratio
 solving problems using
exact trigonometric
ratios for 30°, 45° and
60° (Applying strategies)
MS5.3.2
 proving and using the
relationship between the
sine and cosine ratios of
complementary angles in
right-angled triangles
cos A  sin 90  A
sin A  cos90  A
 proving that the tangent
ratio can be expressed as
a ratio of the sine and
cosine ratios
tan  
Graphs of y = sin x,
y = cos x and y = tan x
(page 280)
Ex 7H Graphs of y = sin x,
y = cos x and y = tan x
(page 280)
Radian measurement
(page 282)
WE 23, 24
Ex 7I Radian
measurement (page 283)
Summary (page 284)
Chapter review (page 286)
Maths Quest challenge
(page 281)
Mathcad: Graphs of
y = sin x, y = cos x and
y = tan x (page 280)
Excel: Graphs of y = sin x,
y = cos x and y = tan x
(page 280)
SkillSHEET 7.9: Changing
degrees to radians
(page 283)
‘Test yourself’ multiple
choice questions
Topic tests (2)
8
Mathcad: Degrees and
radians (page 283)
sin 
cos
MS5.3.2
 drawing the sine and
cosine curves for at least
0  A  180
 asking questions about
how trigonometric ratios
change as the angle
increases from 0° to
180° (Applying
strategies, Reasoning)
 recognising that if
sin A ≥ 0 then there are
two possible values for
A, given 0°≤ A≤ 180°
(Applying strategies,
Reasoning)