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Solution 4.3:1b

From Förberedande kurs i matematik 1

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FIGURE1 FIGURE2
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<center> [[Image:4_3_1_b.gif]] </center>
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the line
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<math>{y=\sin \pi }/{7}\;</math>
<math>{y=\sin \pi }/{7}\;</math>
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the line
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<math>{y=\sin \pi }/{7}\;</math>
<math>{y=\sin \pi }/{7}\;</math>

Revision as of 10:14, 29 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.


Image:4_3_1_b.gif

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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