Trigonometry question finding the sin and tan

Question

If angle $\alpha$ is reflex, and $\cos \alpha = -\frac{9}{41}$, without using a calculator, evaluate

(a) $\sin \alpha$
(b) $\tan \alpha$
(c) $\cos (\alpha - 180\deg)$ .

Answer 1

(a) You know $\cos(\alpha)$, so you can use $\sqrt{\sin^2(\alpha)+\cos^2(\alpha)}=1$ to solve for $\sin^2(\alpha)$. $\alpha$ is reflex, so $\sin(\alpha) < 0$, so you'll want to go with the negative solution.

(b) You know $\sin(\alpha)$ and $\cos(\alpha)$. Just plug into the formula for $\tan(\alpha)$ and evaluate.

(c) I'm assuming it means $1800^{\circ}$? $1800(\text{mod}360) = 0$, so the angle is essentially the same (you're just making full trips around the circle). So, $\cos(\alpha) = \cos(\alpha-1800)$. And you already know $\cos(\alpha)$.