Solution 4.4:2b

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The equation
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The equation <math>\cos x= 1/2</math> has the solution <math>x=\pi/3</math> in the first quadrant, and the symmetric solution <math>x = 2\pi -\pi/3 = 5\pi/3</math> in the fourth quadrant.
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<math>\cos x={1}/{2}\;</math>
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has the solution
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<math>x={\pi }/{3}\;</math>
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in the first quadrant, and the symmetric solution
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<math>x={2\pi -\pi }/{3}\;={5\pi }/{3}\;</math>
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in the fourth quadrant.
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[[Image:4_4_2_b.gif|center]]
[[Image:4_4_2_b.gif|center]]
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Angle
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If we add multiples of <math>2\pi</math> to these two solutions, we obtain all the solutions
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<math>{\pi }/{3}\;</math>
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Angle
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<math>{5\pi }/{3}\;</math>
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If we add multiples of
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<math>2\pi </math>
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to these two solutions, we obtain all the solutions
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<math>x={\pi }/{3}\;+2n\pi </math>
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and
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<math>x={5\pi }/{3}\;+2n\pi </math>
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{{Displayed math||<math>x = \frac{\pi}{3}+2n\pi\qquad\text{and}\qquad x = \frac{5\pi }{3}+2n\pi\,,</math>}}
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where
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where ''n'' is an arbitrary integer.
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<math>n</math>
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is an arbitrary integer.
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Current revision

The equation \displaystyle \cos x= 1/2 has the solution \displaystyle x=\pi/3 in the first quadrant, and the symmetric solution \displaystyle x = 2\pi -\pi/3 = 5\pi/3 in the fourth quadrant.

If we add multiples of \displaystyle 2\pi to these two solutions, we obtain all the solutions

\displaystyle x = \frac{\pi}{3}+2n\pi\qquad\text{and}\qquad x = \frac{5\pi }{3}+2n\pi\,,

where n is an arbitrary integer.

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