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Section 1.6 : Solving Trig Equations with Calculators, Part II

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. These will require the use of a calculator so use at least 4 decimal places in your work.

Find all the solution(s) to the following equations. These will require the use of a calculator so use at least 4 decimal places in your work.

1. \(3 - 14\sin \left( {12t + 7} \right) = 13\) Solution
2. \(3\sec \left( {4 - 9z} \right) - 24 = 0\) Solution
3. \(4\sin \left( {x + 2} \right) - 15\sin \left( {x + 2} \right)\tan \left( {4x} \right) = 0\) Solution
4. \(\displaystyle 3\cos \left( {\frac{{3y}}{7}} \right)\sin \left( {\frac{y}{2}} \right) + 14\cos \left( {\frac{{3y}}{7}} \right) = 0\) Solution
5. \(7{\cos ^2}\left( {3x} \right) - \cos \left( {3x} \right) = 0\) Solution
6. \(\displaystyle {\tan ^2}\left( {\frac{w}{4}} \right) = \tan \left( {\frac{w}{4}} \right) + 12\) Solution
7. \(4{\csc ^2}\left( {1 - t} \right) + 6 = 25\csc \left( {1 - t} \right)\) Solution
8. \(4y\sec \left( {7y} \right) = - 21y\) Solution
9. \(10{x^2}\sin \left( {3x + 2} \right) = 7x\sin \left( {3x + 2} \right)\) Solution
10. \(\displaystyle \left( {2t - 3} \right)\tan \left( {\frac{{6t}}{{11}}} \right) = 15 - 10t\) Solution