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IGCSE Additional Math10.1. Use the six trigonometric functionsTopic Practice

10.1. Use the six trigonometric functions

CAIE IGCSE Additional Math 10.1. Use the six trigonometric functions question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Additional Math practice aligned to CAIE, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

Question 6(a)

[Maximum number: 3]
Question image

The diagram shows an equilateral triangle ABC with side a.
M is the midpoint of AC and angle AMB=90∘A M B=90^{\circ}.
Use the diagram to find sec⁡30∘\sec 30^{\circ}.

Question 9

[Maximum number: 11]

In this question all lengths are in centimetres.

Question image

The diagram shows triangle ABC which has area 253 cm2\frac{2 \sqrt{5}}{3} \mathrm{~cm}^{2}. Angle A is acute.

Question 9(a)

(a)

Find the exact value of sin⁡A\sin A.

[ 3 ]

Question 9(b)

(b)

Find the exact value of cos⁡A\cos A and hence find the exact value of x.

[ 5 ]

Question 9(c)

(c)

Find the exact value of sin⁡B\sin B.

[ 3 ]

Question 5

[Maximum number: 4]

DO NOT USE A CALCULATOR IN THIS QUESTION.

In this question, all lengths are in centimetres.

Question 5(a)

(a)

You are given that cos⁡120∘=−12,sin⁡120∘=32\cos 120^{\circ}=-\frac{1}{2}, \quad \sin 120^{\circ}=\frac{\sqrt{3}}{2} and tan⁡120∘=−3\tan 120^{\circ}=-\sqrt{3}.

In the triangle ABC,AB=53−6,BC=53+6\mathrm{ABC}, A B=5 \sqrt{3}-6, B C=5 \sqrt{3}+6 and angle ABC=120∘A B C=120^{\circ}. Find AC , giving your answer in the form aba \sqrt{b} where a and b are integers greater than 1 .

Question 5(b)

(b)

You are given that cos⁡30∘=32,sin⁡30∘=12\cos 30^{\circ}=\frac{\sqrt{3}}{2}, \quad \sin 30^{\circ}=\frac{1}{2} and tan⁡30∘=13\tan 30^{\circ}=\frac{1}{\sqrt{3}}.

In the triangle PQR,PQ=3+25\mathrm{PQR}, P Q=3+2 \sqrt{5} and angle PQR=30∘P Q R=30^{\circ}. Given that the area of this triangle is 2+554\frac{2+5 \sqrt{5}}{4}, find QR , giving your answer in the form c+d5c+d \sqrt{5}, where C and d are integers.

[ 4 ]

Question 7

[Maximum number: 7]

DO NOT USE A CALCULATOR IN THIS QUESTION.

You may use the following trigonometrical ratios.
sin⁡60∘=32,sin⁡45∘=22\sin 60^{\circ}=\frac{\sqrt{3}}{2}, \sin 45^{\circ}=\frac{\sqrt{2}}{2}cos⁡60∘=12,cos⁡45∘=22\cos 60^{\circ}=\frac{1}{2}, \quad \cos 45^{\circ}=\frac{\sqrt{2}}{2}tan⁡60∘=3,tan⁡45∘=1\tan 60^{\circ}=\sqrt{3}, \quad \tan 45^{\circ}=1

Question 7(a)

(a)

Given that the area of triangle ABC is 3+34\frac{3+\sqrt{3}}{4}, show that sin⁡75∘=6+24\sin 75^{\circ}=\frac{\sqrt{6}+\sqrt{2}}{4}.

[ 5 ]

Question 7(b)

(b)

Hence find the exact length of AC.

[ 2 ]
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