A LevelMathsEdexcelPureFlashcardsTrigonometryModelling with Trigonometric Functions

Modelling with Trigonometric Functions (Edexcel A Level Maths: Pure): Flashcards

Exam code: 9MA0

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A model is given by $h = 5 + 3 \sin (2 t)$ . What are its maximum and minimum values?
$8$ and $2$ .
Because $\sin$ is bounded by $- 1$ and $1$ , the term $3 \sin (2 t)$ ranges from $- 3$ to $3$ .
For a model of the form $\sin (q t + r)$ , the period is:
$T = \frac{360 °}{______}$ , or $\frac{2 π}{______}$ in radians
$T = \frac{360 °}{q}$ , or $\frac{2 π}{q}$ in radians
The $r$ shifts the graph along but has no effect at all on how often it repeats.
What does the period of a model tell you about the situation?
How long it takes for the behaviour to repeat exactly once.
For a tide model with $t$ in hours, a period of $12$ means the pattern comes round every $12$ hours.
Why might you simplify a trigonometric model before interpreting it?
Because the behaviour is far easier to read from a single term than from two.
Writing $a \sin t + b \cos t$ in harmonic form, for instance, makes both the maximum and the period immediate.
True or False?
In a trigonometric model, the variable is usually an angle.
False.
It is usually time, most often written $t$ .
The trigonometric function is there because the situation repeats, not because anything is rotating.

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