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Solution 4.3:1b

From Förberedande kurs i matematik 1

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m (Lösning 4.3:1b moved to Solution 4.3:1b: Robot: moved page)
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{{NAVCONTENT_START}}
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Because the sine value for an angle is equal to the angle's
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<center> [[Image:4_3_1_b.gif]] </center>
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<math>y</math>
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-coordinate on a unit circle, two angles have the same sine value only if they have the same <math>y</math>-coordinate. Therefore, if we draw in the angle
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<math>{\pi }/{7}\;</math>
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on a unit circle, we see that the only angle between
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<math>{\pi }/{2}\;</math>
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and
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<math>\pi </math>
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which has the same sine value lies in the second quadrant, where the line
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<math>{y=\sin \pi }/{7}\;</math>
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cuts the unit circle.
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<center> [[Image:4_3_1b.gif]] </center>
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{{NAVCONTENT_STOP}}
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FIGURE1 FIGURE2
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the line
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<math>{y=\sin \pi }/{7}\;</math>
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the line
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<math>{y=\sin \pi }/{7}\;</math>
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 +
 
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Because of symmetry, we have that this angle is the reflection of the angle
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<math>{\pi }/{7}\;</math>
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in the
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<math>y</math>-axis, i.e.
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<math>v=\pi -{\pi }/{7}\;={6\pi }/{7}\;</math>.

Revision as of 11:59, 12 September 2008

Because the sine value for an angle is equal to the angle's y -coordinate on a unit circle, two angles have the same sine value only if they have the same y-coordinate. Therefore, if we draw in the angle 7 on a unit circle, we see that the only angle between 2 and which has the same sine value lies in the second quadrant, where the line y=sin7 cuts the unit circle.


FIGURE1 FIGURE2 the line y=sin7 the line y=sin7


Because of symmetry, we have that this angle is the reflection of the angle 7 in the y-axis, i.e.

v=−7=67.

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