Practice Exam 3 - Chapter 6
Name:
Instructions:
Give yourself 50 minutes to complete this practice exam.
Justify each answer.
Each answer has equal weight.
1. Determine whether the Law of Cosines is needed to solve the triangle.
(Answer either “Yes” or “No.”)
A = 72◦ , B = 50◦ , a = 10.2
2. Determine whether the Law of Cosines is needed to solve the triangle.
(Answer either “Yes” or “No.”)
a = 6.0, b = 4.2, c = 2.1
3. Determine whether the Law of Cosines is needed to solve the triangle.
(Answer either “Yes” or “No.”)
C = 107◦ , a = 34, b = 55
4. Solve the triangle. A = 20◦ , C = 40◦ , b = 6.0.
5. A triangle has B = 60◦ , a = 5, c = 6. Use the Law of Cosines to
determine the exact length of b.
6. A triangle has a = 4, b = 10, C = 100◦ . Find the area.
For #7, #8, and #9, use ~u = h2, 5i and ~v = h−10, 3i.
7. Find ~u + ~v .
8. Find ~u − ~v .
9. Find −6~u − 3~v .
10. Find the component form of the vector ~v with the conditions that the
initial point of ~v is (−8, 3) and the terminal point of ~v is (4, −11).
11. Find a unit vector in the direction of ~u = h−9, 20i.
12. Find the angle between the vectors ~u = h−1, 5i and ~v = h3, −2i.
13. Are the vectors ~u = h6, 10i and ~v = h−5, 3i orthogonal?
14. Find the projection of ~u = h4, 5i onto ~v = h1, 10i.
15. Write the complex number z = −3 + 3i in trigonometric form.
16. Write the complex number z = 7 (cos(60◦ ) + i sin(60◦ )) in standard
form.
17. Find the indicated power of the complex number.
3
5π
5π
2 cos
+ i sin
6
6
18. Find the indicated power of the complex number.
(5 + 5i)−1
19. Find the third roots of 2i.
20. Find all solutions of the equation x4 − i = 0.