6.1 Pythagoras' theorem
The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.
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IGCSE Maths: Trigonometry
Topic 6 of the Cambridge IGCSE Mathematics (0580) syllabus: from Pythagoras' theorem to the sine and cosine rules and three dimensions. Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.
The 6 parts of the topic
Each part with one practice question, made by the same engine your child plays. Parts marked Extended are for the Extended paper only.
6.2 Right-angled triangles: sides and angles with sin, cos and tan; angles of elevation and depression
From the top of a cliff, the angle of depression of a boat is 27°.
What is the angle of elevation of the cliff top from the boat?
- 27°
- 54°
- 63°
- 153°
Show the answer
27°. The angle of depression is measured down from the HORIZONTAL at the top; the angle of elevation up from the horizontal at the bottom. The two horizontals are parallel, so these are alternate angles: both 27°.
6.3 Exact trigonometric values Extended
tan θ = √3
θ is between 0° and 90°. Find θ.
- 60°
- 30°
- 45°
- 120°
Show the answer
60°. From the exact values of the 30°, 45° and 60° triangles: θ = 60°.
6.4 Trigonometric graphs and equations Extended
What is the smallest value of cos x?
- −90
- 0
- −1
- 180
Show the answer
−1. The cosine graph goes between 1 and −1; the lowest point is −1, at 180°.
6.5 Non-right-angled triangles: sine rule, cosine rule, area as half ab sin C Extended
In triangle ABC, a = 3 cm, b = 5 cm and c = 7 cm.
Find angle C.
- 60°
- 90°
- 120°
- 150°
Show the answer
120°. cos C = (a² + b² − c²) ÷ 2ab = (9 + 25 − 49) ÷ 30 = −0.5, so C = 120°. A negative cosine means an obtuse angle.
6.6 Pythagoras and trigonometry in three dimensions Extended
A cuboid measures 6 cm by 12 cm by 4 cm.
Find the length of the diagonal through its middle.
- 14 cm
- 11 cm
- 22 cm
- 13.4 cm
Show the answer
14 cm. d² = 6² + 12² + 4² = 196, and √196 = 14 cm.
The mistakes that cost the most marks
Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.
Adds or subtracts the sides instead of their squares
Pythagoras works on the SQUARES of the sides.
Forgets the final square root
a² + b² gives c², not c. One more step.
Puts the second solution in the wrong quadrant
Sketch the graph, or use the rule for each function: sin gives 180 − x, cos gives 360 − x, tan gives x + 180.
Puts tan upside down
tan = opposite ÷ adjacent. The side facing the angle goes on top.
Swaps sine and cosine
sin 30° = cos 60° = 1/2. Learn the two special triangles, and check which ratio was given.
Writes the fraction upside down
The bottom number is how many equal parts the whole is cut into.
Uses only two of the three lengths
In 3D the diagonal uses all three: d² = length² + width² + height².
Uses an edge instead of the diagonal in 3D
The line's shadow on the base is the diagonal of the base: find it with Pythagoras first.
Other IGCSE Maths topics
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