Has my teacher been wrong here

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SUMMARY

The discussion centers on a disagreement regarding the application of trigonometric identities in a mathematical problem. The teacher deducted points for incorrectly applying the cosine formula, specifically altering the numerator. The correct transformation of the sine function is highlighted as \(\sin(t) = -\cos(t - 3\pi / 2)\), clarifying the misunderstanding surrounding the use of sine and cosine functions in this context.

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http://i28.tinypic.com/qz54aw.jpg

he reduced 2 points
and put s on the numerator making it cosine formula.
also i clearly transformed sinus
 
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Probably it is because
[tex]\sin(t) = -\cos(t - 3\pi / 2)[/tex]
and not
[tex]-\sin(t - 3\pi / 2)[/tex]
 

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