Question
2. \( \cos 116^{\circ} \) Answer: \( \frac{1}{1-m} \) \( \sqrt{1-m^{2}} \) \( -\sqrt{1-m^{2}} \) \( -m \) Final check
Ask by Crawford Wood.
Mar 14,2025 17:31
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Tutor-Verified Answer
Answer
\[
\cos 116^\circ = -\sqrt{1 - m^{2}}
\]
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Beyond the Answer
Did you know that the cosine function has roots dating back to ancient times? The Babylonians already had methods to calculate trigonometric ratios over 4,000 years ago! They used a base-60 system to devise tables that would allow sailors and astronomers to make sense of angles, laying the groundwork for what we now know as trigonometry.
When dealing with cosine values like \( \cos 116^{\circ} \), it's often helpful to remember the unit circle! Since 116 degrees is in the second quadrant, the cosine will be negative. Visualizing angles in the unit circle can clarify why \( \cos 116^{\circ} = -\cos(116^{\circ} - 180^{\circ}) \) leads us to find a simpler equivalent using special angles!
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