- Mathematics Advanced
- Year 12
Trigonometric Functions
approx. 15 hrs
5 topics
32 concepts
Proficiency in Trigonometric Functions is critical to attaining a successful outcome in your HSC examinations.
approx. 15 hrs
5 topics
32 concepts
Proficiency in Trigonometric Functions is critical to attaining a successful outcome in your HSC examinations.
The Year 12 Trigonometric Functions for Mathematics Advanced program is aligned with the NSW Mathematics Senior syllabus. In this program, we explain to students how to use circular measure when applying techniques from the study of trigonometry, geometry and calculus to solve a variety of questions ranging in complexity.
This learning program is made up of the following 5 topics, broken down into 32 concepts.
Converting degrees to radians
Converting radians to degrees
Using the area of a segment formula to find unknown quantities
Using the arc length formula to find unknown quantities
Finding the area of a sector using radians
Finding the length of an arc using radians
Finding the area of a segment
Using the area of a sector formula to find unknown quantities
Approximations to sin x, cos x, tan x, when x is small
Trigonometric equations for angles of any magnitude in radians
Exact values in radians
Use the result for the function (sin x)/x for the limit as x approaches zero
Finding the amplitude of sine or cosine functions
Sketch trigonometric functions with translation
Sketch trigonometric functions with dilation
Finding the period of trigonometric functions
Sketch trigonometric functions with multiple transformations
Differentiate trigonometric functions involving the quotient rule
Finding the volume of solids of revolution using techniques of integration involving the trigonometric functions
Finding the anti-derivative of a trigonometric function by considering a derivative
Integrals involving trigonometric substitution
Integrals of the type f '(x)(f(x))^n dx
Differentiate trigonometric functions involving the chain rule
Integration of (sinx)^2 and (cosx)^2
Differentiate trigonometric functions involving the product rule
Integrating basic trigonometric expressions
Finding the area of regions using techniques of integration involving the trigonometric functions
Application of the derivative of the trigonometric functions
Using the reverse chain rule to integrate trigonometric functions
Differentiate trigonometric functions with linear arguments
Product rule of differentiation
Quotient rule of differentiation
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