CAIE A-Level Mathematics AS 1.5.2 Exact Trig Values Questions

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

Exam points

Use the exact sine, cosine and tangent values for standard angles such as 30°, 45° and 60° to obtain exact answers.
Evaluate trigonometric expressions at related angles using symmetry and identities, retaining exact fractional or surd values.

[Maximum number: 5]

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

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

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CAIE A-Level Mathematics AS 1.5.2 Exact Trig Values Questions question 1