CAIE A-Level Mathematics 1.5.2 Exact trig values

Practise using exact trig values for 30°, 45°, 60° and related angles to keep answers in exact surd or fractional form.

Exam points

use exact sin, cos or tan values for related angles instead of decimal approximations

[Maximum number: 5]

For the case where angle $B A C=\frac{1}{6} \pi$ radians, find k correct to 4 significant figures.

$\triangle A D E=\frac{1}{2}(k a)^{2} \sin \frac{\pi}{6}$
M1
Attempt to find the area of $\triangle A D E$ .
$\frac{1}{4} k^{2} a^{2}$
A1
OE.
Sector $A B C=\frac{1}{2} a^{2} \frac{\pi}{6}$
B1
$2 \times \frac{1}{4} k^{2} a^{2}=\frac{1}{2} a^{2} \frac{\pi}{6}$
M1
OE. For $2 \times \triangle A D E=$ sector A B C with at least one
correct area.
$k=\left(\sqrt{\frac{\pi}{6}}\right)=0.7236$
A1

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1.5.2—Exact trig values question 1