Solution 4.3:1b

From Förberedande kurs i matematik 1

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.