MathTV Topic - Additional Topics in Trigonometry

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Math Topics

Precalculus
Additional Topics in Trigonometry

1
The Law of Sines

Problem 1

Solve the triangle in Figure 9.

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Gordon

Stephanie

Julieta

Problem 2

Solve the triangle in Frigure 10.

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Gordon

Stephanie

Julieta

Problem 3

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Gordon

Stephanie

Julieta

Problem 4

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Gordon

Stephanie

Julieta

Problem 5

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Gordon

Stephanie

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

Stephanie

Julieta

Problem 7

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

Stephanie

Julieta

2
The Law of Cosines

Problem 1

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

Stephanie

Julieta

Problem 2

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

Breylor

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

Stephanie

Julieta

Problem 4

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

Stephanie

Julieta

Problem 5

Find the area of a triangle that has sides of length 8,5, and 9.

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Gordon

Stephanie

Julieta

3
Polar Coordinates

Problem 1

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Shelby

Breylor

Julieta

Problem 2

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Shelby

Breylor

Julieta

Problem 3

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Shelby

Breylor

Julieta

Problem 4

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Shelby

Breylor

Julieta

Problem 5

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Shelby

Breylor

Julieta

Problem 6

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Shelby

Breylor

Julieta

4
Graphs of Polar Equations

Problem 1

Sketch the graph of r = 4.

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Shelby

Breylor

Julieta

Problem 2

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Shelby

Breylor

Julieta

Problem 3

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Shelby

Breylor

Julieta

Problem 4

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Shelby

Breylor

Julieta

Problem 5

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Shelby

Julieta

Problem 6

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Shelby

Breylor

Julieta

Problem 7

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Shelby

Breylor

Julieta

5
Vectors

Problem 1

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Shelby

Nathan

Julieta

Problem 2

Find the components of the vector u with magnitude 6 and direction angle 117\(^{\circ}\).

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Shelby

Nathan

Julieta

Problem 3

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Shelby

Nathan

Julieta

Problem 4

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Shelby

Nathan

Julieta

Problem 5

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Shelby

Nathan

Julieta

Problem 6

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Shelby

Nathan

Julieta

Problem 7

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Shelby

Nathan

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

Nathan

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

Nathan

Julieta

6
Dot Product of Vectors

Problem 1

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Stephanie

Nathan

Julieta

Problem 2

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Stephanie

Nathan

Julieta

Problem 3

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Stephanie

Nathan

Julieta

Problem 4

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Stephanie

Nathan

Julieta

Problem 5

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Stephanie

Nathan

Julieta

Problem 6

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

Nathan

Julieta

Problem 7

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Stephanie

Nathan

Julieta

7
Trigonometric Form of a Complex Number

Problem 1

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Stephanie

Nathan

Julieta

Problem 2

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Stephanie

Breylor

Julieta

Problem 3

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Saba

Stephanie

Julieta

Problem 4

Find the two square roots of 1 â€“ i.

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Stephanie

Julieta

Problem 5

Find all the fifth roots of 1.

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Stephanie

Breylor

Julieta

CHOOSE A TOPIC

1 The Law of Sines

2 The Law of Cosines

3 Polar Coordinates

4 Graphs of Polar Equations

5 Vectors

6 Dot Product of Vectors

7 Trigonometric Form of a Complex Number

1
The Law of Sines

2
The Law of Cosines

3
Polar Coordinates

4
Graphs of Polar Equations

5
Vectors

6
Dot Product of Vectors

7
Trigonometric Form of a Complex Number