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Section 1-4 : Solving Trig Equations

Without using a calculator find the solution(s) to the following equations. If an interval is given find only those solutions that are in the interval. If no interval is given find all solutions to the equation.

  1. \(4\sin \left( {3t} \right) = 2\) Solution
  2. \(4\sin \left( {3t} \right) = 2\) in \(\displaystyle \left[ {0,\frac{{4\pi }}{3}} \right]\) Solution
  3. \(\displaystyle 2\cos \left( {\frac{x}{3}} \right) + \sqrt 2 = 0\) Solution
  4. \(\displaystyle 2\cos \left( {\frac{x}{3}} \right) + \sqrt 2 = 0\) in \(\left[ { - 7\pi ,7\pi } \right]\) Solution
  5. \(4\cos \left( {6z} \right) = \sqrt {12} \) in \(\displaystyle \left[ {0,\frac{\pi }{2}} \right]\) Solution
  6. \(\displaystyle 2\sin \left( {\frac{{3y}}{2}} \right) + \sqrt 3 = 0\) in \(\displaystyle \left[ { - \frac{{7\pi }}{3},0} \right]\) Solution
  7. \(8\tan \left( {2x} \right) - 5 = 3\) in \(\displaystyle \left[ { - \frac{\pi }{2},\frac{{3\pi }}{2}} \right]\) Solution
  8. \(16 = - 9\sin \left( {7x} \right) - 4\) in \(\displaystyle \left[ { - 2\pi ,\frac{{9\pi }}{4}} \right]\) Solution
  9. \(\displaystyle \sqrt 3 \tan \left( {\frac{t}{4}} \right) + 5 = 4\) in \(\left[ {0,4\pi } \right]\) Solution
  10. \(\sqrt 3 \csc \left( {9z} \right) - 7 = - 5\) in \(\displaystyle \left[ { - \frac{\pi }{3},\frac{{4\pi }}{9}} \right]\) Solution
  11. \(\displaystyle 1 - 14\cos \left( {\frac{{2x}}{5}} \right) = - 6\) in \(\displaystyle \left[ {5\pi ,\frac{{40\pi }}{3}} \right]\) Solution
  12. \(\displaystyle 15 = 17 + 4\cos \left( {\frac{y}{7}} \right)\) in \(\left[ {10\pi ,15\pi } \right]\) Solution