Solution 4.4:1a

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In the unit circle's first quadrant, there is one angle whose sine value equals
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In the unit circle's first quadrant, there is one angle whose sine value equals 1/2 and that is <math>v = \pi/6\,</math>.
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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>.
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[[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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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 ''x''-axis as <math>v=\pi/6</math> makes with the positive ''x''-axis, i.e. the other angle is <math>v = \pi - \pi/6 = 5\pi/6\,</math>.
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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>
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Current revision

In the unit circle's first quadrant, there is one angle whose sine value equals 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 x-axis as \displaystyle v=\pi/6 makes with the positive x-axis, i.e. the other angle is \displaystyle v = \pi - \pi/6 = 5\pi/6\,.

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