Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 cos180 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 cos90 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)