1. For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle, and the sign of the ratio. \( \begin{array}{ll}\text { a) } \sin \frac{3 \pi}{4} & \text { d) } \sec \frac{5 \pi}{6} \\ \text { b) } \cos \frac{5 \pi}{3} & \text { e) } \cos \frac{2 \pi}{3} \\ \text { c) } \tan \frac{4 \pi}{3} & \text { f) } \cot \frac{7 \pi}{4}\end{array} \)

| Trigonometric Ratio | Quadrant | Related Acute Angle | Sign | |---------------------|----------|---------------------|------| | \( \sin \frac{3 \pi}{4} \) | II | \( \frac{\pi}{4} \) | Positive | | \( \cos \frac{5 \pi}{3} \) | IV | \( \frac{\pi}{3} \) | Positive | | \( \tan \frac{4 \pi}{3} \) | III | \( \frac{\pi}{3} \) | Positive | | \( \sec \frac{5 \pi}{6} \) | II | \( \frac{\pi}{6} \) | Negative | | \( \cos \frac{2 \pi}{3} \) | II | \( \frac{\pi}{3} \) | Negative | | \( \cot \frac{7 \pi}{4} \) | IV | \( \frac{\pi}{4} \) | Positive |