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# solving triangle and complex number in polar coordinates

Please see attached file for full problem description.
1. B = 54 degrees, C = 112, and b = 18

2. Solve the equation on the interval [0, 2pi]: (cosx)^2 + 2 cos x + 1 = 0

3. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
C = 110°, a = 5, b = 11

4. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
B = 43 degrees, C = 107, b = 14

5 of 25: Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 20 mph in a direction 330°. The second sails at 34 mph in a direction 220°. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats?

6: A vector v has initial point P1 and P2. Write v in terms of ai + bj: P1 = (-5, 1); P2 = (6, 3)

7: Test the equation for symmetry with respect to the give axis, line, or pole: r = 4 cos(theta); the polar axis

8: Solve the problem: cos(5x/2) + cos(3x/2)

9: Use the given vectors to find the specified scalar: v = 10i + 5j; Find v ? v.

10: Find the absolute value of the complex number: z = 9 - 5i

11. Solve the equation on the interval [0, 2pi]:

12. Find the product of the complex numbers. Leave answer in polar form.
z1 = 5(cos 20 + i sin 20), z2 = 4(cos 10 + i sin 10)

13. Find the exact value by using a difference identity: sin 15

14. Use the given information to find the exact value of the expression:
Find cos (2, theta), csc (theta) = 5/3, theta lies n quadrant II.

15. Find another representation, (r, theta), for the point under the given conditions.

16. Find the solutions of the equation: 2 cos(theta) + 1 = 0

17. Use the given information to find the exact value of the expression.
Find cos (2theta), sin(theta)= 20/29, theta lies in quadrant I.

18. Use a half-angle formula to find the exact value of the expression: sin 22.5

19.Express the product as a sum or difference: sin 6x cos 2x

20. Complete the identity:

21. Solve the equation on the interval [0, 2pi]:
sin 4x = sqrt(3) /2

22. Complete the identity: cos(a + b)cos(a- b)

23. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
B = 18, C = 113, b = 44

24. Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no trianagle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measure to the nearest degree.
A = 30 degrees, a = 20, b = 40

25. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
B = 29, C = 112, b = 35

#### Solution Summary

The solution shows how to solve the triangle using law of sines and cosines. It also explains the complex number in polar coordinates.

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