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\( 180 ^ { \circ } - \frac { 360 ^ { \circ } - ( \hat { r } + \hat { \Delta } ) } { 2 } \)

Ask by Ball Summers. in Greece
Feb 19,2025

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Para simplificar la expresión \( 180^\circ - \frac{360^\circ - (\hat{r} + \hat{\Delta})}{2} \), primero simplificamos la parte dentro de los paréntesis. Sin embargo, sin conocer los valores de \( \hat{r} \) y \( \hat{\Delta} \), no podemos simplificarla completamente.

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Bonus Knowledge

Did you know that the concept of angles and their measurements dates back to ancient civilizations? The Egyptians and Babylonians were among the first to develop systems for measuring angles, and they utilized a 360-degree system because of the approximately 360 days in a year. This fascinating historical backdrop gives us a rich context for understanding geometry today! In real-world applications, angles like the one mentioned can be crucial in fields such as architecture and engineering. When designing buildings or bridges, understanding angle relationships ensures that structures are both aesthetically pleasing and structurally sound. Knowing how to manipulate these angles helps architects create innovative designs that withstand the test of time.

Related Questions

8. Simplify without using a calculator. (8.1) \( \frac{\sin \left(180^{\circ}-x\right) \cdot \tan \left(360^{\circ}-x\right)}{\cos \left(80^{\circ}-x\right)} \times \frac{\cos \left(-180^{\circ}-x\right)}{\cos \left(360^{\circ}+x\right) \sin \left(360^{\circ}-x\right)} \) \( 8.2 \frac{\cos 135^{\circ} \sin 160^{\circ}}{\sin 225^{\circ} \cos 70^{\circ}} \) (8.3) \( \frac{\sin (-\theta)+\cos 120^{\circ}+\tan \left(-180^{\circ}-\theta\right)}{\sin ^{2} 225^{\circ}-\tan (-\theta)-\cos \left(90^{\circ}+\theta\right)} \) B.4 \( 4^{x} \frac{\sin 247^{\circ} \cdot \tan 23^{\circ} \cdot \cos 113^{\circ}}{\sin \left(-157^{\circ}\right)} \) (8.5) \( \frac{3 \cos 150^{\circ} \cdot \sin 270^{\circ}}{\tan \left(-45^{\circ}\right) \cdot \cos 600^{\circ}} \) 8.6) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}+x\right)}{\sin (-x)}-\sin y \cdot \cos \left(90^{\circ}-y\right) \) \( 8.7 \frac{\tan 30^{\circ} \cdot \sin 60^{\circ} \cdot \cos 25^{\circ}}{\cos 135^{\circ} \cdot \sin \left(-45^{\circ}\right) \cdot \sin 65^{\circ}} \) 6.8) \( \frac{\tan \left(180^{\circ}-x\right) \cdot \sin \left(90^{\circ}-x\right)}{\cos \left(90^{\circ}+x\right)}-\frac{\cos \left(180^{\circ}-x\right)}{\sin \left(90^{\circ}+x\right)} \) \( 8.9 \frac{\sin 189^{\circ}}{\tan 549^{\circ}}-\frac{\cos ^{2}\left(-9^{\circ}\right)}{\sin 99^{\circ}} \) Solving trigonometric equations (no calculators) (1.) If \( \sin \mathrm{A}=\frac{-3}{5} \) and \( 0^{\circ}<\mathrm{A}<270^{\circ} \) determine the value of: \( 1.1 \cos A \) \( 1.2 \tan A \). (2.) If \( -5 \tan \theta-3=0 \) and \( \sin \theta<0 \), determine: \( 2.1 \sin ^{2} \theta^{\circ} \) \( 2.25 \cos \theta \) \( 2.3 \quad 1-\cos ^{2} \theta \) 3. If \( 13 \cos \theta+12=0 \) and \( 180^{\circ}<\theta<360^{\circ} \), evaluate: \( 3.2 \tan \theta \) \( 3.1 \sin \theta \cos \theta \) \( 3.3 \sin ^{2} \theta+\cos ^{2} \theta \). (4.) If \( 3 \tan \theta-2=0 \) and \( \theta \in\left[90^{\circ} ; 360^{\circ}\right] \), determine, the value of \( \sqrt{13}(\sin \theta-\cos \theta \) (5.) If \( \cos 52^{\circ}=k \) as illustrated in the diagram, determine each of the following i
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