s
er
ap
eP
m
e
tr
.X
w
w
w
om
.c
Scheme of work – Cambridge IGCSE® Mathematics (US) 0444
Unit 8: Trigonometry (Extended)
Recommended prior knowledge
All of Core and particularly Core 8. Only those parts of the learning objectives or notes and exemplars not included in the core units are itemised, so this document
should be read alongside the core document. It is also necessary for students to have understood Extended 2 (2.11).
Context
There are five Core geometry units and this is the fifth of five Extended geometry units. Once Core 8, the other prior experience for Core 8 and Extended 2 (2.11)
are completed this unit can be slotted in at any point. It is probably best taught as a whole but used to revise some of the Core 8.
Outline
The unit extends the knowledge of Core 8 so be aware that examination questions that relate to aspects of Core 8 may have a greater degree of challenge as they
combine with other areas of mathematics. This unit covers trigonometry in all four quadrants, the special case ratios for some angles, Sine Rule, Cosine Rule and
Area of Triangle using an angle.
Syllabus ref
Learning objectives
Suggested teaching activities
8.1
Know the exact values for the
trigonometric ratios of 0°, 30°,
45°, 60°, 90°
Teaching activities
In Unit Core 8, this task was recommended. Returning to this task can
show the case 0°, 30°, 45°, 60°, 90°. Draw a 10cm circle on a coordinate
grid, (centre the origin), marking off 10° angles from the origin to intersect
with the circumference and noting their coordinates, Plotting the xcoordinate divided by 10 against angle, the y-coordinate divided by 10
against the angle, and the x-coordinate divided by the y-coordinate against
the angle either for the first quadrant.
CCSS:
G-SRT6
G-SRT8
Learning resources
Using the special triangles below gives the values a different way.
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
1
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
isosceles triangle equal side of unit length
∴ x = 45°
hypotenuse =
1
x
2
∴ sin(45°) = cos(45°) =
1
1
2
equilateral triangle sides 2 units
∴ y = 60° and z = 30°
z
2
base of right angled triangle is 1
2
height is
3
∴ sin(30°) = cos(60°) =
y
∴sin(60°) = cos(30°) =
8.2
CCSS:
G-SRT7
Extend sine and cosine
values to angles between 0°
and 360°
Explain and use the
relationship between the sine
and cosine of complementary
angles
Graph and know the
properties of trigonometric
functions
8.3
CCSS:
G-SRT11
Sine Rule
1
2
3
2
Both the visualizations will help students reconstruct diagrams to remind
themselves which is which if they have difficulty learning these.
Teaching activities
This task has already been recommended in Core 8 and for 8.1 above
completing the full circle and using co-ordinates will show the positive and
negative values in the correct places.
Draw a 10cm circle on a coordinate grid, (centre the origin), marking off 10°
angles from the origin to intersect with the circumference and noting their
coordinates, Plotting the x-coordinate divided by 10 against angle, the ycoordinate divided by 10 against the angle, and the x-coordinate divided by
the y-coordinate against the angle either for the first quadrant or for all 360°
Drawing any right angled triangle and labelling the lengths a, b, c the
angles α and and then writing out statements of the trig functions for α
and should convince students about the equivalence of sine and cosine
of complementary angles.
Notes and exemplars
Formula will be given. ASA, SSA (ambiguous case included where the
angle is obtuse).
General guidance
Students need to know the conventions of labelling a triangle to be able to
apply the formula - with the lower case letter for the length of the side
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
www.youtube.com/watch?v=APNkWrDU1k
www.bbc.co.uk/schools/gcsebitesize/mat
hs/shapes/furthertrigonometryhirev1.sht
ml
2
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
opposite the upper case angle. Some students find it hard to find opposite
sides so instead describe it as the side that isn’t the two arms of the angle.
Past Paper 41 June 2011 Q1bii
(syllabus 0580)
Teaching activities
Use the video to help you construct the proof using white or blackboard
more sequentially and completing the trio of equivalences.
Ask students to solve missing side and angle problems that require Sine
Rule including bearings problems.
8.4
Cosine Rule
CCSS:
G-SRT11
Notes and exemplars
Formula will be given. SAS, SSS.
General guidance
Students need to know the conventions of labelling a triangle to be able to
apply the formula - with the lower case letter for the length of the side
opposite the upper case angle. Some students find it hard to find opposite
sides so instead describe it as the side that isn’t the two arms of the angle.
www.bbc.co.uk/schools/gcsebitesize/mat
hs/shapes/furthertrigonometryhirev2.sht
ml
Past Paper 41 June 2011 Q1bi
(syllabus 0580)
Past Paper 42 June 2011 Q3c
(syllabus 0580)
Teaching activities
From the video for Sine Rule there is a link to the Cosine Rule. Link the
proof solving Quadratic Equations using the formula Extended 2 (2.11)
Ask students to solve missing side and angle problems that require Cosine
Rule including bearings problems.
8.5
CCSS:
G-SRT9
v1 2Y01
Area of triangle
Finally give students a bank of mixed problems so that they can distinguish
when to use Sine Rule and when to use Cosine rule, i.e. distinguishing
between cases where you have the included angle and the case where you
don’t have an angle from the others.
Notes and exemplars
Formula will be given.
www.bbc.co.uk/schools/gcsebitesize/mat
hs/shapes/furthertrigonometryhirev3.sht
ml
General guidance
Students need to know the conventions of labelling a triangle to be able to
apply the formula - with the lower case letter for the length of the side
opposite the upper case angle. Some students find it hard to find opposite
sides so instead describe it as the side that isn’t the two arms of the angle.
Cambridge IGCSE Mathematics (US) 0444
3
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
You can prove the rule if this is productive but students need practice
applying the rule and distinguishing this rule from the sine and cosine rule.
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
4