Solution 4.4:1a

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m (Lösning 4.4:1a moved to Solution 4.4:1a: Robot: moved page)
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In the unit circle's first quadrant, there is one angle whose sine value equals
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<center> [[Image:4_4_1a.gif]] </center>
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<math>\frac{1}{2}</math>
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and that is
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<math>v={\pi }/{6}\;</math>.
[[Image:4_4_1_a.gif|center]]
[[Image:4_4_1_a.gif|center]]
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From the figures, we see that there is a further angle with the same sine value and it lies in the second quadrant. Because of symmetry, it makes the same angle with the negative
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<math>x</math>
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-axis as
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<math>v={\pi }/{6}\;</math>
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makes with the positive
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<math>x</math>
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-axis, i.e. the other angle is
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<math>v=\pi -{\pi }/{6}\;={5\pi }/{6}\;</math>

Revision as of 11:58, 30 September 2008

In the unit circle's first quadrant, there is one angle whose sine value equals \displaystyle \frac{1}{2} and that is \displaystyle v={\pi }/{6}\;.

From the figures, we see that there is a further angle with the same sine value and it lies in the second quadrant. Because of symmetry, it makes the same angle with the negative \displaystyle x -axis as \displaystyle v={\pi }/{6}\; makes with the positive \displaystyle x -axis, i.e. the other angle is \displaystyle v=\pi -{\pi }/{6}\;={5\pi }/{6}\;

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