1. The problem asks whether $\cos(87\pi + a)$ is positive or negative. 2. Recall the cosine addition formula and periodicity: cosine has period $2\pi$, so $$\cos(87\pi + a) = \cos(87\pi)\cos(a) - \sin(87\pi)\sin(a).$$ 3. Since $\sin(87\pi) = 0$ (because $87\pi$ is a multiple of $\pi$), this simplifies to $$\cos(87\pi + a) = \cos(87\pi)\cos(a).$$ 4. Next, evaluate $\cos(87\pi)$. Since $\cos(k\pi) = (-1)^k$ for integer $k$, and $87$ is odd, $$\cos(87\pi) = (-1)^{87} = -1.$$ 5. Therefore, $$\cos(87\pi + a) = -1 \cdot \cos(a) = -\cos(a).$$ 6. The sign of $\cos(87\pi + a)$ is the opposite of the sign of $\cos(a)$. Final answer: $\cos(87\pi + a)$ has the opposite sign of $\cos(a)$, so it is positive if $\cos(a)$ is negative, and negative if $\cos(a)$ is positive.