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Section 1-3 : Trig Functions

Determine the exact value of each of the following without using a calculator.

Note that the point of these problems is not really to learn how to find the value of trig functions but instead to get you comfortable with the unit circle since that is a very important skill that will be needed in solving trig equations.

  1. \(\displaystyle \tan \left( {\frac{{3\pi }}{4}} \right)\)
  2. \(\displaystyle \sin \left( {\frac{{7\pi }}{6}} \right)\)
  3. \(\displaystyle \sin \left( { - \frac{{3\pi }}{4}} \right)\)
  4. \(\displaystyle \cos \left( {\frac{{4\pi }}{3}} \right)\)
  5. \(\displaystyle \cot \left( {\frac{{5\pi }}{4}} \right)\)
  6. \(\displaystyle \sin \left( { - \frac{{5\pi }}{6}} \right)\)
  7. \(\displaystyle \sec \left( { - \frac{\pi }{6}} \right)\)
  8. \(\displaystyle \cos \left( {\frac{{5\pi }}{4}} \right)\)
  9. \(\displaystyle \cos \left( {\frac{{11\pi }}{6}} \right)\)
  10. \(\displaystyle \csc \left( {\frac{{11\pi }}{6}} \right)\)
  11. \(\displaystyle \cot \left( { - \frac{{4\pi }}{3}} \right)\)
  12. \(\displaystyle \cos \left( { - \frac{\pi }{4}} \right)\)
  13. \(\displaystyle \csc \left( {\frac{{2\pi }}{3}} \right)\)
  14. \(\displaystyle \sec \left( {\frac{{17\pi }}{6}} \right)\)
  15. \(\displaystyle \sin \left( { - \frac{{23\pi }}{3}} \right)\)
  16. \(\displaystyle \tan \left( {\frac{{31\pi }}{6}} \right)\)
  17. \(\displaystyle \cos \left( { - \frac{{15\pi }}{4}} \right)\)
  18. \(\displaystyle \sec \left( { - \frac{{23\pi }}{4}} \right)\)
  19. \(\displaystyle \cot \left( {\frac{{11\pi }}{4}} \right)\)