The Unit Circle

  1. Find the coterminal angle in $[0, 2\pi]$ for each of the following angles.  solution

    2. \(-60^0, \quad \dfrac{9\pi}{4}, \quad -\dfrac{7\pi}{4}, \quad \dfrac{11\pi}{3}, \quad -\dfrac{31\pi}{6}, \quad 690^0 \)

    Video: Filling out the Unit Circle and Finding the exact Values of the Trig Functions.

  2. Find the exact value of the following trigonometric functions.

    3. (a) $\cos \left(150^{\circ}\right) \qquad \cot \left(-150^{\circ}\right) \qquad \csc \left(210^{\circ}\right) \qquad \sin \left(330^{\circ}\right)$   solution

    (b) $\tan \left(-\frac{7 \pi}{4}\right) \qquad \cos \left(\frac{7 \pi}{6}\right) \qquad \sec \left(-\frac{2 \pi}{3}\right) \qquad \sin \left(-\frac{5 \pi}{6}\right)$   solution

    (c) $\tan \left(\frac{9 \pi}{4}\right) \qquad \sin \left(\frac{19 \pi}{4}\right) \qquad \cot \left(-\frac{11 \pi}{6}\right) \qquad \csc \left(-\frac{7\pi}{4}\right) $   solution