Question 575726
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What is the cosine of the angle whose sine is 1/2?


Look on the unit circle, recalling that the  *[tex \Large y]-coordinate of the point of intersection of the terminal side ray and the unit circle is the sine of the angle and the  *[tex \Large x]-coordinate is the cosine:


<img src="http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png">


The angle whose sine is 1/2 is either *[tex \Large \frac{\pi}{6}\ +\ 2k\pi] in which case *[tex \Large \cos\left(\frac{\pi}{6}\ +\ 2k\pi\right)\ =\ \frac{\sqrt{3}}{2}] or *[tex \Large \frac{5\pi}{6}\ +\ 2k\pi] in which case  *[tex \Large \cos\left(\frac{5\pi}{6}\ +\ 2k\pi\right)\ =\ -\frac{\sqrt{3}}{2}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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