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Solution 4.4:1b

From Förberedande kurs i matematik 1

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Current revision (13:07, 10 October 2008) (edit) (undo)
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The easiest angle to find is
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The easiest angle to find is <math>v = \pi/3</math> in the first quadrant. When we draw the unit circle, we see that the angle which makes the same angle with the positive ''x''-axis as <math>v=\pi/3</math>, but is under the ''x''-axis, also has a cosine value of 1/2 (same ''x''-coordinate).
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<math>v={\pi }/{3}\;</math>
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in the first quadrant. When we draw the unit circle, we see that the angle which makes the same angle with the positive
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<math>x</math>
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-axis as
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<math>v={\pi }/{3}\;</math>, but is under the
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<math>x</math>
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-axis, also has a cosine value of
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<math>{1}/{2}\;</math>
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(same
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<math>x</math>
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-coordinate).
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[[Image:4_4_1_b.gif|center]]
[[Image:4_4_1_b.gif|center]]
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There are thus two angles,
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There are thus two angles, <math>v=\pi/3</math> and <math>v=2\pi - \pi/3 = 5\pi/3</math> which have their cosine value equal to 1/2.
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<math>v={\pi }/{3}\;</math>
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and
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<math>v=2\pi -{\pi }/{3}\;={5\pi }/{3}\;</math>
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which have their cosine value equal to
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<math>\frac{1}{2}</math>.
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Current revision

The easiest angle to find is v=3 in the first quadrant. When we draw the unit circle, we see that the angle which makes the same angle with the positive x-axis as v=3, but is under the x-axis, also has a cosine value of 1/2 (same x-coordinate).

There are thus two angles, v=3 and v=2−3=53 which have their cosine value equal to 1/2.

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