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LearnEdexcelYMA012018 specificationWMA11 · Pure Mathematics 1Trigonometry

WMA11 · Module

Trigonometry

8 subtopics≈ 300 min in total

Start the module: Exact values and the unit circle Open graphing calculator

Exact values and the unit circle
How sine, cosine and tangent are defined for any angle using the unit circle, the CAST rule for signs, and the exact values at $30^\circ$ , $45^\circ$ and $60^\circ$ that you need without a calculator.
≈ 40 min
Radians
What a radian is, why mathematicians prefer it to the degree, and how to convert between the two, with exact values in terms of $\pi$ .
≈ 30 min
Sine rule, cosine rule and area
For any triangle: the sine rule links each side to its opposite angle; the cosine rule handles two sides and the included angle, or three sides; and the area is $\tfrac12ab\sin C$ . Watch for the ambiguous case when using the sine rule to find an angle.
≈ 40 min
Graphs and transformations
The shapes of $y=\sin x$ , $y=\cos x$ and $y=\tan x$ , their symmetries, and how $a$ , $b$ , $c$ and $d$ in $y=a\sin(b(x-c))+d$ stretch and shift them. Then use the graphs to count solutions and model things that repeat.
≈ 45 min
Arc length and sector area
Why the formulae $s=r\theta$ and $A=\tfrac12r^2\theta$ work, how to use them for perimeters, and how to work backwards from a length or an area to the radius or angle.
≈ 35 min
Radians, arcs and sectors
One radian is the angle where the arc equals the radius, so a full turn is $2\pi$ radians. In radians the formulas become beautifully simple: arc length $s=r\theta$ and sector area $A=\tfrac12r^2\theta$ . A segment is a sector minus a triangle.
≈ 30 min
Graphs of sine, cosine and tangent
Sine and cosine are waves with period $360^\circ$ ( $2\pi$ ) between $-1$ and $1$ ; tangent repeats every $180^\circ$ with asymptotes. Transform them like any graph: $a\sin x$ changes the height, $\sin bx$ squeezes the period to $\dfrac{360^\circ}b$ , and $\sin(x+c)$ slides it left.
≈ 35 min
Segments, chords and composite shapes
Cutting a sector with a chord: the segment formula, chord lengths, and the exam-style shaded regions built from sectors, triangles and tangents.
≈ 45 min