Solution 4.3:3b

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The angle <math>\pi-v</math> makes the same angle with the negative ''x''-axis as the angle <math>v</math> makes with the positive ''x''-axis and this means that <math>\pi-v</math> is the reflection of <math>v</math> in the ''y''-axis.
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Under such reflection, the angle's ''y''-coordinate does not change (but the ''x''-coordinate changes sign) and therefore <math>\sin (\pi-v) = \sin v = a\,</math>.

Current revision

The angle \displaystyle \pi-v makes the same angle with the negative x-axis as the angle \displaystyle v makes with the positive x-axis and this means that \displaystyle \pi-v is the reflection of \displaystyle v in the y-axis.

Under such reflection, the angle's y-coordinate does not change (but the x-coordinate changes sign) and therefore \displaystyle \sin (\pi-v) = \sin v = a\,.

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