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### Section 1-5 : Solving Trig Equations with Calculators, Part I

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. $$\displaystyle 2 - 14\sin \left( {\frac{t}{3}} \right) = 5$$
2. $$4\cos \left( {4x} \right) + 8 = 10 - \cos \left( {4x} \right)$$
3. $$2\tan \left( {3w} \right) + 3 = 25$$
4. $$\displaystyle 2\sin \left( {\frac{{3x}}{5}} \right) - \frac{7}{5} = \frac{1}{5}$$ in $$\left[ {0,15} \right]$$
5. $$\displaystyle 1 = 3 + 8\cos \left( {\frac{w}{2}} \right)$$ in $$\left[ { - 20,5} \right]$$
6. $$\displaystyle 45\sin \left( {\frac{x}{2}} \right) - 9 = 7\sin \left( {\frac{x}{2}} \right) + 17$$ in $$\left[ { - 10,20} \right]$$
7. $$\displaystyle \frac{2}{3} = 4 - 3\sec \left( {11x} \right)$$ in $$\left[ {0,1} \right]$$
8. $$3\sin \left( {4v} \right) + 18\cos \left( {4v} \right) = 0$$ in $$\left[ {2,5} \right]$$
9. $$\displaystyle 2\left( {\cos \left( {\frac{{2t}}{7}} \right) + 3} \right) = 7\cos \left( {\frac{{2t}}{7}} \right) + 6$$ in $$\left[ { - 10,30} \right]$$
10. $$\displaystyle \frac{1}{2}\csc \left( {\frac{y}{3}} \right) - \frac{{10}}{7} = \frac{3}{{14}}$$ in $$\left[ {0,32} \right]$$
11. $$\displaystyle 31 = 1 + 40\cos \left( {\frac{t}{8}} \right)$$ in $$\left[ { - 50,60} \right]$$
12. $$15\csc \left( {15x} \right) + 14 = 20 - 12\csc \left( {15x} \right)$$ in $$\left[ {1,2} \right]$$
13. $$\displaystyle \frac{1}{2}\cos \left( {6t} \right) + 3 = 1 + \frac{1}{3}\cos \left( {6t} \right)$$ in $$\left[ {0,5} \right]$$
14. $$\displaystyle 4\left( {1 - 2\sec \left( {\frac{z}{5}} \right)} \right) = 12$$ in $$\left[ {0,15} \right]$$
15. $$\displaystyle 11 - 7\sin \left( {\frac{{2x}}{{13}}} \right) = 23 - 19\sin \left( {\frac{{2x}}{{13}}} \right)$$ in $$\left[ { - 60,60} \right]$$