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Precalculus
Additional Topics in Trigonometry

1
The Law of Sines

Problem  1
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Solve the triangle in Figure 9.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  2
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Solve the triangle in Frigure 10.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  3
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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  4
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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  5
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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  6

The angles of elevation from points A and B to the top of a plam tree are both 80\(^{\circ}\). See Figure 14. Points A and B are 15 feet apart, and the base of the tree lies on the line between them. Find the height of the tree.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  7
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A tour boat travels 10 miles due north from its starting point and then travels in the direction S40\(^{\circ}\)W on its second leg of the tour. If the boat is currently 15 miles from its starting point, how far has it traveled on the second leg? Round your final answer to two decimal places.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta espanol spanish
Julieta

2
The Law of Cosines

Problem  1
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The sides of triangle ABC in Figure 3 are

a = 4, b = 2, c = 5.

Find the angles of the trianlge.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  2
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Find the length of the unknown side of the triangle in Figure 4. Also, find the measures of all the angles.

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Stephanie
Stephanie
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  3

Two motorboats start from the same point. One of them travels in the direction N30\(^{\circ}\)W at 45 miles per hour, and the other heads due east at 35 miles per hour. How far apart are the boats after one hour?

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  4
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Find the area of a triangle if the lengths of two of its sides are 12 and 7 and their included angle is 65\(^{\circ}\).

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta
Problem  5
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Find the area of a triangle that has sides of length 8,5, and 9.

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Gordon cc
Gordon
Stephanie
Stephanie
Julieta cc espanol spanish
Julieta

3
Polar Coordinates

Problem  1
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  2
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  3
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  4
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  5
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  6
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta

4
Graphs of Polar Equations

Problem  1

Sketch the graph of r = 4.

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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  2
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  3
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Shelby
Shelby
Breylor
Breylor
Julieta cc espanol spanish
Julieta
Problem  4
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  5
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Shelby
Shelby
Julieta
Julieta
Julieta espanol spanish
Julieta
Problem  6
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  7
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Shelby
Shelby
Breylor
Breylor
Julieta espanol spanish
Julieta

5
Vectors

Problem  1
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  2
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Find the components of the vector u with magnitude 6 and direction angle 117\(^{\circ}\).

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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  3
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  4
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  5
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  6
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  7
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Shelby
Shelby
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  8

Using a specially designed golf flag, a golfer finds that the wind is blowing through the course at a speed of 12 miles per hour in the direction N40\(^{\circ}\) W Express the wind velocity in vector form, rounded to two decimal places.

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Shelby
Shelby
Nathan
Nathan
Julieta espanol spanish
Julieta
Problem  9

A boat traels in the direction S18\(^{\circ}\)E at a speed of 15 miles per hour. It encourters a wind blowing north to south at a speed of 10 miles per hour. Find the resulting speed and direction of the boat.

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Stephanie cc
Stephanie
Nathan
Nathan
Julieta espanol spanish
Julieta

6
Dot Product of Vectors

Problem  1
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  2
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  3
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  4
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  5
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  6
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A man is pushing a lawn mover handle with a force of 35 pounds. If the angle the handle makes with the horizontal is 40\(^{\circ}\), how much work is done in moving the lawn mower a distance of 150 feet on level ground?

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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta
Problem  7
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta cc espanol spanish
Julieta

7
Trigonometric Form of a Complex Number

Problem  1
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Stephanie cc
Stephanie
Nathan
Nathan
Julieta espanol spanish
Julieta
Problem  2
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Choose instructor to watch:
Stephanie cc
Stephanie
Breylor
Breylor
Julieta espanol spanish
Julieta
Problem  3
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Saba cc
Saba
Stephanie
Stephanie
Julieta espanol spanish
Julieta
Problem  4
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Find the two square roots of 1 – i.

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Stephanie cc
Stephanie
Julieta
Julieta
Julieta espanol spanish
Julieta
Problem  5
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Find all the fifth roots of 1.

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Stephanie cc
Stephanie
Breylor
Breylor
Julieta espanol spanish
Julieta