Home > Subjects > Mathematics > Level 3 - calculus > 3.3 Trigonometry (AS90637) > Achievement criteria
- Subject: Mathematics
- AS: 90637
- Level: 3
- Credits: 4
- Internal
Calculus 3.3 Solve problems and equations involving trigonometric functions
Achievement criteria
The level of achievement that you reach is decided by the questions that you answer correctly.
Achievement
- You solve straightforward problems with models involving trigonometric functions.
- Problems will involve trigonometric functions of the form:
- AsinB(x + C) + D, where C, D may be zero
- AsinB(x + C) + D, where C, D may be zero
- AtanB(x + C) + D, where C, D may be zero.
- Solution of the problems may require knowledge of amplitude, period, and frequency.
- Solve straightforward trigonometric equations.
- Equations to be solved will be selected from the following forms:
- AsinB(x + C) = K
- AsinBx = K
- AcosB(x + C) = K
- AcosBx = K
- AtanB(x + C) = K
- Atan Bx = K
- You are expected to use both degrees and radians.
Achievement with Merit
- You need to reach Achievement.
- You model situations using trigonometric functions and solve trigonometric problems.
- You will form an equation for the model and use the model to solve problems. The form of the model will be selected from:
- y = AsinB(x + C) + D
- y = AcosB(x + C) + D
- y = AtanB(x + C) + D.
- Information that allows you to find A, B, C, or D may be given or collected.
- The information may be in the form of data.
- Only one of C and D may be 0.
- You use trigonometric manipulation which could include proving trigonometric identities or solving more difficult equations and may involve the following:
- reciprocal relationships
- Pythagorean identities
- compound angle formulae
- double angle formulae
- sum and product formulae and combinations of these.
- Where manipulation involves solving equations, you may be asked to provide:
- a general solution
- solutions within a specified domain.
Achievement with Excellence
- You need to reach Achievement with Merit.
- Apply knowledge of trigonometric relationships to solve complex problem(s).
- Problem(s) will require a chain of reasoning and may involve:
- a proof
- developing a formula from a given starting point(s)
- rewriting a trigonometric expression in terms of a single trigonometric function
- identifying and rectifying a flaw in reasoning
- evaluation of the model (limitations, improvements, long-term accuracy) where data has been collected
- solving more complex equations
- solving 3-D trigonometric problems.
- You will be expected to choose and apply appropriate trigonometric relationships. (Knowledge of the sine and cosine rule may be required.)
