For an acute angle θ, cos(270° − θ) is equal to:

270° is an odd multiple of 90°, so the cosine changes into a sine; and for an acute θ the angle 270° − θ lies in the third quadrant, where the cosine is negative. Hence cos(270° − θ) = −sinθ. Check at θ = 30°: cos240° = −0.5 = −sin30°. Keeping the name 'cosine' because the angle was built from 270° gives ±cosθ, and losing the quadrant sign gives +sinθ.