CAIE IGCSE Additional Math 10.5 Solve Trigonometric Equations Questions

Practise Cambridge IGCSE Additional Mathematics by solving trigonometric equations with identities, substitutions and complete interval solutions.

Exam points

Solve trigonometric equations over a stated degree or radian interval.
Use identities, substitutions and factorisation to reduce equations to standard trigonometric forms.
List all valid solutions in the interval and exclude undefined or extraneous values.

[Maximum number: 10]

(a)

Solve the equation $\tan ^{2} 2 x-4 \tan 2 x=0$ for $0^{\circ} \leqslant x \leqslant 180^{\circ}$ .

Solve the equation $\tan ^{2} 2 x-4 \tan 2 x=0$ for $0^{\circ} \leqslant x \leqslant 180^{\circ}$ .

[ 4 ]

$[\tan2x=0]$ any two of 2x=0,180,360x=0,90,180 nfww and no extras from $\tan2x=0$ $[\tan2x=4]$ $2x=75.96\ldots$ or $255.96\ldots$ x=38.0 or 37.9818..., and x=128.0 or 127.9818..., with no extras

(b)

Solve the equation $\operatorname{cosec}(y+1.2)=4$ , where y is in radians and -5<y<2.

[ 6 ]

$\sin(y+1.2)=\frac14$
Two correct values for y+1.2 soi:
$y+1.2=0.252680\ldots,\quad y+1.2=\pi-0.252680\ldots=2.88891\ldots,\quad y+1.2=-\pi-0.252680\ldots=-3.39427\ldots$
M1 for any one correct value.
$y=-0.947\ldots$ , $1.68891\ldots$ , $-4.59427\ldots$ , and no others in -5<y<2

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CAIE IGCSE Additional Math 10.5 Solve Trigonometric Equations Questions question 1

Question (a)

Question (b)