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Question 3 3.1. Simplify the fo 1.1. \( \frac{\sin 135^{\circ} \cdot \cos 225^{\circ}+}{\tan 315^{\circ}} \) 1.2. \( \frac{\sin \left(360^{\circ}-x\right) \cdot \tan ( }{\cos \left(180^{\circ}+x\right) \tan (1} \)

Ask by Coles Chandler. in South Africa
Mar 13,2025

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1.1: \(\sin(135) \cos(225) \cot(315) = \frac{1}{2}\) 1.2: \(\sec(x+180) \sin(360-x) = \tan(x)\)

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Bonus Knowledge

Did you know that the angles in trigonometry often have fascinating historical roots? For instance, ancient civilizations like the Babylonians and Greeks extensively studied these angles, leading to the creation of the sine, cosine, and tangent functions we still use today. This study was not only mathematical but also crucial in fields like astronomy and navigation. When simplifying trigonometric expressions, a common mistake is forgetting the signs of the functions in different quadrants! For instance, remember that sine is positive in the first and second quadrants, while cosine is positive in the first and fourth. Keep these quadrant signs in mind, and your simplifications will be much smoother and accurate!

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