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Solution 4.4:3a

From Förberedande kurs i matematik 1

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The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type <math>\cos x = a\,</math>.
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<center> [[Image:4_4_3a.gif]] </center>
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In this case, we can see directly that one solution is <math>x = \pi/6\,</math>. Using the unit circle, it follows that <math>x = 2\pi - \pi/6 = 11\pi/6\,</math> is the only other solution between <math>0</math> and <math>2\pi\,</math>.
[[Image:4_4_3_a.gif|center]]
[[Image:4_4_3_a.gif|center]]
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We obtain all solutions to the equation if we add multiples of <math>2\pi</math> to the two solutions above,
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{{Displayed math||<math>x = \frac{\pi}{6} + 2n\pi\qquad\text{and}\qquad x = \frac{11\pi}{6} + 2n\pi\,,</math>}}
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where ''n'' is an arbitrary integer.

Current revision

The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type cosx=a.

In this case, we can see directly that one solution is x=6. Using the unit circle, it follows that x=2−6=116 is the only other solution between 0 and 2.

We obtain all solutions to the equation if we add multiples of 2 to the two solutions above,

x=6+2nandx=611+2n

where n is an arbitrary integer.

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