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