it will depend on the implementation and processor if it's faster to calculate simultaneous sin and cos of a given angle, or sin(w) and sin(w+pi/2), but you are

it will depend on the implementation and processor if it's faster to calculate simultaneous sin and cos of a given angle, or sin(w) and sin(w+pi/2), but you are right you could do it all with sin or cos only. But there is already a different thing called a discrete cosine transform :)