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# Trigonometry

The basics, the laws and relationships, and roots of unity.

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Right triangle $$\triangle ABC$$ has a right angle at $$B$$, and $$\angle BAC = 30^{\circ} = \frac{\pi}{6}$$. Find $\sin\angle BAC + \cos\angle BCA.$

In triangle $$\triangle ABC$$, $$AB = 3, AC = 4$$, and $$\angle BAC = \frac{\pi}{2}$$. What is $$BC$$?

Let $$ABC$$ be an equilateral triangle. Point $$D$$ lies on $$BC$$ so that $$\angle BAD = 15^{\circ}$$. Find $$\frac{[BAD]}{[CAD]}$$.

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