- Mathematics Advanced
- Year 10
Trigonometry
approx. 18 hrs
10 topics
34 concepts
Develop mastery in Trigonometry to enhance your understanding of and performance in Mathematics.
approx. 18 hrs
10 topics
34 concepts
Develop mastery in Trigonometry to enhance your understanding of and performance in Mathematics.
This program covers the fundamental principles of measurement with triangles and is aligned to the Australian curriculum. In Year 10 Advanced Trigonometry, students develop skills in selecting and applying rules and processes to find unknown angles and side lengths. These are the skills required to solve problems involving bearings and angles of elevation and depression. In addition, students acquire a deeper understanding of trigonometric ratios in terms of the unit circle and its application to solving angles of any magnitude.
This learning program is made up of the following 10 topics, broken down into 34 concepts.
Define the sine, cosine and tangent ratios for angles in right-angled triangles
Identify the hypotenuse, adjacent sides and opposite sides on a right angles triangle
Rounding angles to the nearest degree, minute or second
Find the size in degrees of unknown angles using SOH CAH TOA in right-angled triangles
Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees
Use the calculator to find unknown angles using sine, cosine and tangent functions
Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees and minutes
Find the size in degrees and minutes of unknown angles using SOH CAH TOA in right-angled triangles
Solve a variety of practical problems involving angles of elevation and depression of right-angled triangles
Construct a bearing diagram from a worded problem
Calculate a bearing from a given diagram
Interpret three-figure (or true) bearings and compass bearings
Solve worded problems involving bearings using SOH CAH TOA
Apply trigonometry in three-dimensions
The four quadrants
Prove the relationships between the sine and cosine ratios of complementary angles in right-angled triangles
Determine the angle of inclination of a line on the Cartesian plane
Prove and apply the tangent ratio identity
Trigonometric ratios of obtuse angles
Determine the possible acute and/or obtuse angle(s), given a trigonometric ratio
Use the unit circle to redefine the sine, cosine and tangent ratios
Using a reference (or related) angle to find angles of any magnitude
Solve simple trigonometric equations involving only sin/cos/tan
Exact values of trigonometric ratios
Converting radians to degrees
Converting degrees to radians
Solve simple trigonometric equations involving only sin/cos/tan using radians
Exact values in radians
Find a side length given the area of a non-right-angled triangle
Use the sine area formula to find the area of a non-right-angled triangle
Use the cosine rule to find unknown sides and angles of a non-right-angled triangle
Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles
Apply the appropriate rule to find unknowns in non-right-angled triangles
Use the sine rule to find unknown sides and angles of a non-right-angled triangle including the ambiguous case
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