Knowledge organisers

Trigonometry: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about trigonometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
Angle of elevation: The angle up from the horizontal to an object.
Bearing: A three-figure angle measured clockwise from north.
Sine rule: a/sin A = b/sin B = c/sin C, for any triangle.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Pythagoras	\(a^2+b^2=c^2\)
SOHCAHTOA	\(\sin\theta=\frac{\text{opp}}{\text{hyp}},\) \(\cos\theta=\frac{\text{adj}}{\text{hyp}},\) \(\tan\theta=\frac{\text{opp}}{\text{adj}}\)
Bearings: measured clockwise from north, written with 3 figures
Exact values	\(\sin30^\circ=\tfrac12,\) \(\cos60^\circ=\tfrac12,\) \(\tan45^\circ=1,\) \(\sin60^\circ=\tfrac{\sqrt3}2,\) \(\sin45^\circ=\tfrac{\sqrt2}2\)
Sine ruleOn the Extended formula list	\(\frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}\)
Cosine ruleOn the Extended formula list	\(a^2=b^2+c^2-2bc\cos A\)
Area of a triangleOn the Extended formula list	\(\tfrac12ab\sin C\)
Obtuse angles	\(\sin(180^\circ-x)=\sin x,\) \(\cos(180^\circ-x)=-\cos x\)

Worked example

A ladder 5 m long leans against a wall with its foot 1.4 m from the wall. Find the angle the ladder makes with the ground.

cos θ = adjacent/hypotenuse = 1.4/5 = 0.28
θ = cos⁻¹(0.28)

Answer: θ = 73.7° (1 d.p.)

Common mistakes

Bearings: the wrong angle, or measured from the wrong line
Calculator set to radians instead of degrees
Using the sine rule when two sides and the angle between them are given (that needs the cosine rule)

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Use Pythagoras' theorem to find a missing side in right-angled triangles and solve problems, including deciding whether a triangle is right-angled.
Solve bearings problems and other two-dimensional problems with Pythagoras and trigonometry, drawing a clear diagram for each.
Sketch and interpret the graphs of y = sin x, y = cos x and y = tan x for 0° ≤ x ≤ 360°, including their key features.
Use the cosine rule to find a missing side, or an angle when all three sides are known, in any triangle.
Find the angle between a line and a plane by identifying the projection of the line onto the plane and a suitable right-angled triangle.
Practise giving exact answers without a calculator, using exact trigonometric values and leaving answers in terms of π.

The printable sheet

Trigonometry knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Trigonometry knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Geometry · Mensuration · Transformations and vectors · Probability · Statistics · All Cambridge IGCSE Maths (0580) organisers