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Welect your answer \[ \begin{array}{l}45^{\circ} \text { and } 225^{\circ} \\ -50^{\circ} \text { and } 150^{\circ} \\ 60^{\circ} \text { and } 300^{\circ} \\ -70^{\circ} \text { and } 290^{\circ} \\ 90^{\circ} \text { and }-90^{\circ}\end{array} \]

Ask by Cole Vargas. in the United States
Feb 03,2025

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Tutor-Verified Answer

Answer

The pair \(-70^\circ\) and \(290^\circ\) are coterminal angles.

Solution

It looks like you're asking to **select the pair of angles that are coterminal**. Coterminal angles are angles that share the same terminal side when drawn in standard position, differing by full rotations of \(360^\circ\). Let's evaluate each pair: 1. **45° and 225°** - Difference: \(225° - 45° = 180°\) - Not coterminal (they are **supplementary angles**). 2. **-50° and 150°** - Difference: \(150° - (-50°) = 200°\) - Not coterminal. 3. **60° and 300°** - Difference: \(300° - 60° = 240°\) - Not coterminal. 4. **-70° and 290°** - To check coterminality: \[ -70° + 360° = 290° \] - Since adding \(360°\) to \(-70°\) gives \(290°\), these angles are **coterminal**. 5. **90° and -90°** - Difference: \(90° - (-90°) = 180°\) - Not coterminal (they are **opposite angles**). **Conclusion:** The pair **\(-70^\circ\) and \(290^\circ\)** are coterminal angles.

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Beyond the Answer

The angles mentioned in your selection span various quadrants of the unit circle. For example, \(45^{\circ}\) and \(225^{\circ}\) represent angles in the first and third quadrants, respectively, where they are a reflection of each other. This symmetry exists due to the properties of the unit circle, which is useful for visualizing trigonometric functions. In practical application, these angles can be useful in fields ranging from engineering to computer graphics. For instance, knowing these angles aids in understanding vectors' direction in a 2D plane, enhancing performance in game development and simulations, where rotations and transformations are pivotal to creating realistic movements and objects!

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