Mathematics

The key is recognizing that sine and cotangent are periodic functions, so you can "unwrap" any angle by adding or subtracting full rotations ($2\pi$) until you land in a familiar range. Once you've reduced $\theta$ to a coterminal angle between $0$ and $2\pi$, you'll recognize a standard position angle whose trig values you know. Then compute both $\sin\theta$ and $\cot\theta = \frac{\cos\theta}{\sin\theta}$ from that reference angle.

The key is recognizing that sine and cotangent are periodic functions, so you can "unwrap" any angle by adding or subtracting full rotations ($2\pi$) until you land in a familiar range. Once you've reduced $\theta$ to a coterminal angle between $0$ and $2\pi$, you'll recognize a standard position angle whose trig values you know. Then compute both $\sin\theta$ and $\cot\theta = \frac{\cos\theta}{\sin\theta}$ from that reference angle.