HEATHCOTE HIGH SCHOOL
YEAR 10 MATHEMATICS PROGRAM
2006
TOPIC:
Trigonometry
OUTCOMES:
Stage 5.3: MS5.3.2 Applies trigonometric relationships, sine rule, cosine rule and area rule in problem solving
(p 141)
SUGGESTED TIME:
CONTENT
Key Ideas for Stage 5.3
1. Determine the exact trigonometric ratios for
30, 45, 60
2. Apply relationships in trigonometry for
complementary angles and tan in terms of sin
and cos
3. Determine trigonometric ratios for obtuse
angles
4. Sketch sine and cosine curves
5. Explore trigonometry with non-right-angled
triangles: sine rule, cosine rule and area rule
6. Solve problems involving more than one
triangle using trigonometry
KNOWLEDGE AND SKILLS
 proving and using the relationship between
the sine and cosine ratios of complementary
angles in right-angled triangles
 proving that the tangent ratio can be
expressed as a ratio of the sine and cosine
ratios
 determining and using exact sine, cosine and
tangent ratios for angles of 30°, 45°, and 60°
 establishing and using the following
relationships for obtuse angles, where
0  A  90 :

cos180
tan 180

 A   cos A
 A   tan A
sin 180  A  sin A
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 drawing the sine and cosine curves for at
least 0  A  180
finding the possible acute and/or obtuse
angles, given a trigonometric ratio
proving the sine rule: In a given triangle ABC,
the ratio of a side to the sine of the opposite
angle is a constant.
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
proving the cosine rule
using the cosine rule to find unknown sides
and angles of a triangle
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Heathcote High School
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687316996
RESOURCES
New Century 10 Advanced Ch
5 p121 – 161, Ch 14 p398 - 420
New Century 10 Intermediate
Ch 13 p310 - 345
Maths Works 10 Intermediate
Ch 12 p430 - 457
TERMINOLOGY
sine, cosine, tangent, sine rule,
cosine rule, complementary, right
angled triangles, ratio, obtuse
angles, acute angles, constant,
relationships, inclination,
coordinate plane, gradient
New Century 10 Adv & Int BLM
6.2 – 6.6
Excel 10 Advanced p59 - 66
WORKING
MATHEMATICALLY
 solve problems, including
practical problems, involving
the sine and cosine rules and
the area rule eg problems
related to surveying or
orienteering
(Applying Strategies)
 recognise 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,
Reasoning)
 explain what happens if the
sine, cosine and area rules
DIAGNOSIS/ASSESSMENT
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 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
Heathcote High School
687316996
are applied in right-angled
triangles (Reasoning)
 ask questions about how
trigonometric ratios change
as the angle increases from
0 to 180 (Questioning)
 recognise that if sin A ≥ 0
then there are two possible
values for A, given 0º ≤ A ≤
180º
(Applying Strategies,
Reasoning)
 find the angle of inclination, θ,
of a line in the coordinate
plane by establishing and
using the relationship
gradient = tan θ (Reasoning,
Reflecting)
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