EduNinja

[Maximum number: 3]

The diagram shows part of the graph of $y=a\cos\left(\frac{x}{b}\right)+c$ , where a, b and c are integers. Find the values of a, b and c.

Figure for Question 1 — CAIE IGCSE Additional Math

[Maximum number: 3]

Figure for Question 2 — CAIE IGCSE Additional Math

The diagram shows the curve $y=a \cos b x+c$ for $-180^{\circ} \leqslant x \leqslant 180^{\circ}$ .
It is given that a, b and c are integers.
Find the values of a, b and c.

[Maximum number: 6]

Solve the equation $2 \sin ^{3} \theta=3 \sin \theta \cos \theta$ for $-\frac{\pi}{2} \leqslant \theta \leqslant \frac{\pi}{2}$ ．

$\sin\theta(2\sin^2\theta-3\cos\theta)=0$ $\sin\theta=0$ , so $\theta=0$ , and no other solutions in range from this factor
$2(1-\cos^2\theta)=3\cos\theta$ oe
Write in solvable form: $-2\cos^2\theta-3\cos\theta+2=0$ oe
Factorises or solves their 3-term quadratic in $\cos\theta$ , e.g. $(2\cos\theta-1)(\cos\theta+2)=0$ $\theta=\pm\frac{\pi}{3}$ or $\pm1.05$ or $\pm1.04719\ldots$ , and no other solutions in range from this factor

CAIE IGCSE Additional Math 10 Trigonometry Topic Practice

Question 1

Question 2

Question 3