- Mathematics Extension 1
- Year 11
Trigonometric Ratios
approx. 14 hrs
8 topics
30 concepts
Build extensive skills in Trigonometric Ratios to optimise academic outcomes.
approx. 14 hrs
8 topics
30 concepts
Build extensive skills in Trigonometric Ratios to optimise academic outcomes.
In Trigonometric Ratios students will develop proficiency in selecting and applying rules and processes to answer a range of questions including trigonometric identities, bearings and non-right-angled trigonometry. Students will be also explore 3D problems, sums and differences of angles and more complex solutions to trigonometric equations.
This learning program is made up of the following 8 topics, broken down into 30 concepts.
Exact values of trigonometric ratios including reciprocal functions
Reciprocal trigonometric functions
Find the exact value of a trigonometric ratio given another trigonometric ratio
Use the unit circle to redefine the sine, cosine and tangent ratios
Use the unit circle and graph trigonometric functions
Compare the features of trigonometric curves, including periodicity and symmetry
Using a reference (or related) angle to find angles of any magnitude
Trigonometric equations with compound angles
Solve trigonometric equations with one trigonometric function across a specified domain using the related angle
The two ratio identities
The three identities for complementary angles
Proving a mix of trigonometric identities
The three Pythagorean identities
Interpret three-figure (or true) bearings and compass bearings
Solve worded problems involving bearings using SOH CAH TOA
Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles
Solve complex bearings problem involving non-right-angled triangles
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
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
3D trigonometry where the base triangle is not right-angled
Finding angles and lengths inside various solids
3D trigonometry where the base triangle is right-angled
Sums and Differences of angles
Application of the t (or half-angle) formula to solve complex trigonometric equations
Auxiliary angle method
Ratios of double angles
General solution of trigonometric equations
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