Trigonometry - Exact Trigonometric Values and the Unit Circle
Trigonometry - Exact Trigonometric Values and the Unit Circle
TGM Original Questions
Without using a calculator, find the exact value of each of the following.
- \( \frac{\sin \frac{\pi}{3} + \cos 0}{\cos \frac{\pi}{3} + \sin \frac{\pi}{6}} \)
- \( \frac{1 + \tan^2 \frac{\pi}{3}}{\sin \frac{\pi}{4} \cos \frac{\pi}{4}} \)
- \( \sin^2 \frac{\pi}{3} + \cos^2 \frac{\pi}{3} \)
- \( \frac{\tan^2 \frac{\pi}{4} - \sin^2 \frac{\pi}{2}}{\cos \frac{\pi}{6} \tan \frac{\pi}{6}} \)
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Answer:(i) \(\frac{\sqrt{3} + 2}{2} \) (ii) \(1\) (iii) \(8\) (iv) \(0\)
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