Precalculus by Richard Wright

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Heaven and earth will pass away, but my words will never pass away. Matthew 24:35 NIV

6-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

  1. How many triangles are formed with the given information: A = 50°, a = 70, b = 100?
  2. Solve the triangle with the given information. Round to two decimal places if necessary.
  3. A = 76°, B = 17°, c = 14
  4. A = 50°, a = 50, b = 60
  5. a = 6, b = 9, c = 10
  6. A = 31°, b = 21, c = 32
  7. This triangle has two solutions. Find angle B in the second solution: A = 80°, a = 69, b = 70.
  8. Find the area of the triangle with a = 7, b = 13, c = 11. Round to two decimal places.
  9. Find the component form of a vector with initial point at (10, 13) and terminal point at (0, 17).
  10. Find a unit vector in the direction of ⟨13, 84⟩.
  11. Let \(\overset{\rightharpoonup}{u} = \langle 20, 15 \rangle\) and \(\overset{\rightharpoonup}{v} = \langle -10, 11 \rangle\), find the following.
  12. \(\overset{\rightharpoonup}{u} + \overset{\rightharpoonup}{v}\)
  13. \(2\overset{\rightharpoonup}{v}\)
  14. \(6\overset{\rightharpoonup}{u} - 3\overset{\rightharpoonup}{v}\)
  15. \(\overset{\rightharpoonup}{u} \cdot \overset{\rightharpoonup}{v}\)
  16. Find the angle between \(\overset{\rightharpoonup}{u}\) and \(\overset{\rightharpoonup}{v}\).
  17. Are the vectors ⟨−2, 4⟩ and \(\left\langle \frac{1}{2}, -1 \right\rangle\) orthogonal, parallel, or neither?
  18. A lawn mower is pushed by exerting a force of 42 pounds on a handle that makes a 30° angle with the horizontal ground. Find the work done by pushing the lawn mower 100 feet.
  19. Write \(z = -9 + 9\sqrt{3}i\) in trigonometric form.
  20. Write \(z = 25\left(\cos \frac{11π}{6} + i \sin \frac{11π}{6}\right)\) in standard form.
  21. Given m = 10(cos 115° + i sin 115°) and n = 2(cos 25° + i sin 25°), find the following and express your solutions in standard form rounded to two decimal places.
  22. m ÷ n
  23. m · n
  24. n2
  25. Find the 2nd roots of \(81\left(-\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i\right)\). Express your answers in standard form rounded to two decimal places.

Answers

  1. No triangle
  2. a = 13.60, b = 4.10, C = 87°
  3. B1 = 66.82°, C1 = 63.18°, c1 = 58.25; B2 = 113.18°, C2 = 16.82°, c2 = 18.88
  4. A = 36.34°, B = 62.72°, C = 80.94°
  5. B = 37.69°, C = 111.31°, a = 17.69
  6. 92.46°
  7. 38.50
  8. ⟨−10, 4⟩
  9. \(\langle \frac{13}{85}, \frac{84}{85} \rangle\)
  10. ⟨10, 26⟩
  11. ⟨−20, 22⟩
  12. ⟨150, 57⟩
  13. −35
  14. 95.40°
  15. Parallel
  16. 3637.31 ft·lbs
  17. \(18\left(\cos \frac{2π}{3} + i \sin \frac{2π}{3}\right)\)
  18. \(\frac{25\sqrt{3}}{2} - \frac{25}{2}i\)
  19. 5i
  20. −15.32 + 12.86i
  21. 2.57 + 3.06i
  22. 3.44 + 8.31i; −3.44 − 8.31i