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Solution 4.3:1b

From Förberedande kurs i matematik 1

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Because the sine value for an angle is equal to the angle's ''y''-coordinate on the unit circle, two angles have the same sine value only if they have the same ''y''-coordinate. Therefore, if we draw in the angle <math>\pi/7</math> on a unit circle, we see that the only angle between <math>\pi/2</math> and <math>\pi</math> which has the same sine value lies in the second quadrant, where the line <math>y = \sin (\pi/7)</math> cuts the unit circle.
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Because of symmetry, we have that this angle is the reflection of the angle <math>\pi/7</math> in the ''y''-axis, i.e. <math>v = \pi - \pi/7 = 6\pi/7\,</math>.

Current revision

Because the sine value for an angle is equal to the angle's y-coordinate on the 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=sin(7) cuts the unit circle.

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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