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Maths Quest General Mathematics NSW HSC Course

Work Program

Chapter 3: Applications of trigonometry

M6: Measurement

Section

/

Content

/ GC tips, Investigations, 10Quick Questions / SkillSHEETS, WorkSHEETS, Test yourself, Topic Tests
(CD-ROM) / Technology applications (CD-ROM) / Prescribed skills, knowledge and understanding
Are you ready? (page80) / SkillSHEETs (page 80)
3.1:Right-angled trigonometry — finding a side length
3.2:Using the inverse trigonometric ratios
3.4:Right-angled trigonometry — finding an angle
3.5:Converting nautical miles and kilometres
3.6:Angle sum of a triangle
3.7:Solving fractional equations
Review of right-angled triangles (page 81)
WE 1, 2, 3
Ex 3A Review of right-angled triangles (page 85) / Right-angled triangles
  • calculating sides and angles using trigonometry in right-angled triangles
/ GC tip— Casio: Using equation solver to find side lengths (page 81)
GC tip — Casio: Using equation solver to find the size of an angle (page 83) / SkillSHEET 3.1: Right-angled trigonometry — finding a side length (page 85)
SkillSHEET 3.2: Using the inverse trigonometric ratios (page 85)
SkillSHEET 3.3: Rounding angles to the nearest degree (page 85)
SkillSHEET 3.4: Right-angled trigonometry — finding the angle (page 85) / Cabri Geometry: Sine, cosine and tangent (page85) /
  • solving problems using trigonometric ratios in one or more right-angled triangles
  • selecting and using appropriate trigonometric ratios and formulae to solve problems
  • preparing diagrams to represent given information where appropriate

Bearings (page 86)
WE 4, 5, 6
Ex 3B Bearings (page 89) / Bearings
  • examining compass bearings and true bearings
  • solving bearings questions by drawing diagrams and using right-angled trigonometry
Obtuse angles
  • examining trigonometric ratios for obtuse angles and determining a pattern
/ Investigation: Trigonometric ratios for obtuse (page 91) / Skillsheet 3.5: Converting nautical miles and kilometres (page 89) /
  • using compass bearings (eight points only) and true bearings (three figure bearings) in problem-solving related to maps and charts
  • establishing the sine, cosine and tangent ratios for obtuse angles from a calculator
  • determining the sign of these ratios for obtuse angles
  • selecting and using appropriate trigonometric ratios and formulae to solve problems
  • preparing diagrams to represent given information where appropriate

The sine rule (page91)
WE 7, 8, 9
Ex 3C Using the sine rule to find side lengths (page 95)
WE 10, 11
Ex 3D Using the sine rule to find angles (page 99) / Sine rule
  • calculating sides using the sine rule
  • calculating angles using the sine rule
  • applying the sine rule to bearings questions
/ Investigation: Derivation of the sine rule (page91)
GC tip — Casio: Using equation solver to solve sine rule problems (sides) (page 93)
GC tip — Casio: Using equation solver to solve sine rule problems (angles) (page 98)
10 Quick Questions 1 (page101) / SkillSHEET 3.6: Angle sum of a triangle (page 95)
SkillSHEET 3.7: Solving fractional equations (page95)
WorkSHEET 3.1 (page 100) / Cabri Geometry: Triangle (page 96) /
  • using the sine rule to find lengths and angles:

  • using appropriate trigonometric ratios and formulae in two-triangle problems where one triangle is right-angled and the diagram is given
  • solving problems involving non-right-angled triangles
  • selecting and using appropriate trigonometric ratios and formulae to solve problems
  • preparing diagrams to represent given information where appropriate

Area of a triangle (page 102)
WE 12, 13
Ex 3E Area of a triangle (page 103) / Area of a triangle
  • calculating the area of a triangle using trigonometry
/
  • calculating area of a triangle using the formula:
  • preparing diagrams to represent given information where appropriate

The cosine rule (page105)
WE 14, 15, 16
Ex 3F Using the cosine rule to find side lengths
(page 109)
WE 17, 18, 19, 20
Ex 3G Using the cosine rule to find angles (page 115) / Cosine rule
  • calculating sides and angles using the cosine rule
/ Investigation: Derivation of the cosine rule (page106)
GC tip — Casio: Using equation solver to solve cosine rule problems (sides) (page 107)
GC tip — Casio: Using equation solver to solve cosine rule problems (angles) (page 112)
10 Quick Questions 2 (page117) /
  • using the cosine rule to find lengths and angles:

or:
  • solving problems involving non-right-angled triangles
  • selecting and using appropriate trigonometric ratios and formulae to solve problems
  • preparing diagrams to represent given information where appropriate

Radial surveys (page118)
WE 21, 22, 23
Ex 3H Radial surveys (page 121) / Surveying
  • carrying out a survey
  • solving surveying problems using trigonometry and/or Pythagoras
/ Investigation: Conducting a radial survey (page122) / WorkSHEET 3.2 (page 122) /
  • conducting radial (both plane table and compass) surveys
  • selecting and using appropriate trigonometric ratios and formulae to solve problems
  • solving problems involving non-right-angled triangle trigonometry, Pythagoras’ theorem and area in offset and radial surveys

Summary (page 123)
Chapter review
(page 125)
Practice examination questions (page 127) / ‘Test yourself’ multiple choice questions (page 128)
Topic tests (2)