Exact Values on the Unit Circle Worksheet with Answer Key

What's on the worksheet

1. Each angle is quadrantal.
   \sec 3\pi\cot\left(-\dfrac{\pi}{2}\right)\csc 450^\circ\tan(-540^\circ)\sec\left(-\dfrac{3\pi}{2}\right)
2. The eight angles below are the multiples of π4 in one turn.
   \theta = 0\theta = \dfrac{\pi}{4}\theta = \dfrac{\pi}{2}\theta = \dfrac{3\pi}{4}\theta = \pi
3. Each angle is a multiple of π6 or π4, but not every fraction is in lowest terms.
   \dfrac{20\pi}{6}\dfrac{12\pi}{4}-\dfrac{22\pi}{6}\dfrac{15\pi}{4}
4. Let θ = 27π4.
5. Carlos writes the six values at θ = 3π2 like this:
6. Evaluate exactly, or explain why the expression has no value.
7. The sixteen angles 0, π6, π4, π3, π2, , 11π6 are the multiples of π6 or π4 with 0 ≤ θ < 2π.