Show All Notes Hide All Notes

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

1. \(7\cos \left( {4x} \right) + 11 = 10\) Solution
2. \(\displaystyle 6 + 5\cos \left( {\frac{x}{3}} \right) = 10\) in \(\left[ {0,38} \right]\) Solution
3. \(\displaystyle 3 = 6 - 11\sin \left( {\frac{t}{8}} \right)\) Solution
4. \(\displaystyle 4\sin \left( {6z} \right) + \frac{{13}}{{10}} = - \frac{3}{{10}}\) in \(\left[ {0,2} \right]\) Solution
5. \(\displaystyle 9\cos \left( {\frac{{4z}}{9}} \right) + 21\sin \left( {\frac{{4z}}{9}} \right) = 0\) in \(\left[ { - 10,10} \right]\) Solution
6. \(\displaystyle 3\tan \left( {\frac{w}{4}} \right) - 1 = 11 - 2\tan \left( {\frac{w}{4}} \right)\) in \(\left[ { - 50,0} \right]\) Solution
7. \(\displaystyle 17 - 3\sec \left( {\frac{z}{2}} \right) = 2\) in \(\left[ {20,45} \right]\) Solution
8. \(12\sin \left( {7y} \right) + 11 = 3 + 4\sin \left( {7y} \right)\) in \(\left[ { - 2, - \frac{1}{2}} \right]\) Solution
9. \(5 - 14\tan \left( {8x} \right) = 30\) in \(\left[ { - 1,1} \right]\) Solution
10. \(\displaystyle 0 = 18 + 2\csc \left( {\frac{t}{3}} \right)\) in \(\left[ {0,5} \right]\) Solution
11. \(\displaystyle \frac{1}{2}\cos \left( {\frac{x}{8}} \right) + \frac{1}{4} = \frac{2}{3}\) in \(\left[ {0,100} \right]\) Solution
12. \(\displaystyle \frac{4}{3} = 1 + 3\sec \left( {2t} \right)\) in \(\left[ { - 4,6} \right]\) Solution