Surveying & Navigation
The tools we use to analyse and model our natural and man-made environment change our perspective of it.
The MYP criteria this unit is marked against.
- Knowing and Understanding
- Communicating
- Applying Mathematics in Real-life Contexts
What this unit covers
The sub-topics taught, in the order the department teaches them.
- General right-angle trigonometry in degrees
- Non-right trigonometry
- Radian measure (EXT)
- Arc lengths and sector areas (in radians for EXT)
- General trig functions
- Unit circle (EXT)
Learning objectives
What students should be able to do by the end of this unit.
Non-right-angle Trigonometry
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- Apply right-angled trigonometry and Pythagoras' theorem to multi-step problems, including 3D.
- Apply the sine rule to find missing sides and angles.
- Apply the cosine rule to find missing sides and angles.
- Apply the area-of-a-triangle formula $\tfrac{1}{2}ab\sin C$.
- Solve problems involving bearings.
- Combine right-angle and non-right-angle trigonometry in surveying / navigation contexts.
- Solve problems involving the ambiguous case of the sine rule.EXT
- Prove the sine rule and the cosine rule.ENR
Radian Measure and the Unit Circle (Extended)
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- Convert between degrees and radians; understand radian measure as arc length on the unit circle.EXT
- Use the full unit circle to define $\sin\theta$, $\cos\theta$ and $\tan\theta$ for any angle.EXT
- Use special triangles to find exact trigonometric values at multiples of $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$.EXT
- Apply negative-angle and complementary-angle identities.EXT
- Apply the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$ and $\tan\theta = \dfrac{\sin\theta}{\cos\theta}$.EXT
- Solve trigonometric equations of the form $\sin x = k$, $\cos x = k$, $\tan x = k$ in radians.EXT
- Calculate arc length, sector area and segment area in radians.EXT
- Calculate arc length, sector area and segment area in degrees.
Trigonometric Modelling
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- Identify periodic behaviour in real-world contexts (tides, daylight, sound, rotating machinery).
- Model periodic phenomena using $y = A \sin(B(x - C)) + D$ and $y = A \cos(B(x - C)) + D$.
- Identify and interpret amplitude, period, mean (vertical shift) and phase shift.
- Fit a sinusoidal model to data using technology.
- Use a fitted model to predict and interpret values in context.
- Investigate transformations of more general set functions and piecewise periodic functions.EXT
- Explore the tangent function.ENR
Practice & review
Targeted practice for each skill, hosted on Dr Frost Maths. Tick when comfortable.
Non-Right Trig
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- Practice on DFM →#465Sine rule (Law of Sines)
- Practice on DFM →#466Cosine rule (Law of Cosines)
- Practice on DFM →#467Area of a triangle using two lengths and the angle between them
Sectors
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- Practice on DFM →#318Arc length of more general sectors
- Practice on DFM →#319Area of more general sectors
Surface Area and Volume
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- Practice on DFM →#234Surface area of a cylinder
- Practice on DFM →#406Surface area of a pyramid, cone or sphere/hemisphere
- Practice on DFM →#408Surface area of more complex compound 3D shapes
Unit Circle [EXT]
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- Practice on DFM →#412Exact trigonometric values
- Practice on DFM →#430Using the unit circle to find trigonometric values above ||90^{\circ}||
- Practice on DFM →#434Solving simple trigonometric equations, e.g. ||\sin(x) = k||, using a graph
- Practice on DFM →#503Solving trigonometric equations, involving ||\sin||, ||\cos|| and ||\tan||, in an interval in degrees
Radians [EXT]
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- Practice on DFM →#584Using radians for arc lengths and areas of sectors, and lengths, angles and areas of triangles
Trig Modelling
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- Practice on DFM →#431Plotting and recognising graphs of trigonometric functions
- Practice on DFM →#448Graph transformations of ||y = f(x+a)|| and ||y = f(x) + a||
- Practice on DFM →#449Graph transformations of ||y = f(-x)|| and ||y = -f(x)||
- Practice on DFM →#450Graph transformations of ||y = f(ax)|| and ||y = af(x)|| (dilations)
- Practice on DFM →#451Combinations of graph transformations
Curated revision materials parents and students can download.
A review pack for this unit is being prepared.
MYP framing
- Focus ATLs
- Communication
- Thinking
- Key concepts
- Form
- Models
- Measure
- Global context
- Orientation in Space and Time