Page 28 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

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7

Trigonometry

OBJECTIVES

Upon completion of chapter 7, the student will be able to—
1. Explain the principles of right triangle trigonometry.
2. Define the three most common trigonometric functions, or ratios: sine,
cosine, and tangent.
3. Use trigonometric functions to find the unknown measurement of one side
of a right triangle when the other two sides or one acute angle and one side
are known.
4. Use a table of trigonometric functions or a scientific calculator to quickly
solve for missing values in triangles.
5. Name the reciprocals of the sine, cosine, and tangent.
6. Determine which trigonometric function to use when solving problems
involving triangles.
7. Solve for unknown measurements of oblique triangles by using trigono-
metric formulas.
8. Find the area of triangles by using trigonometric functions.
9. Apply trigonometric formulas to everyday situations by constructing tri-
angles to represent the situations.
10. Solve problems requiring the use of inverse functions.

INTRODUCTION
Trigonometry is the study of triangles and their use in solving problems. Indeed, B
the word trigonometry derives from the Greek words for triangle measurement.
All triangles have sides and angles, and trigo nom etry deals with the relationship 60°
these sides and angles have to each other. Using trigonometry, unknown data c a
can be found from given, or known, data. For example, surveyors can compute a
distance that they cannot physically measure by determining angles and lengths
with their surveying instruments. Then, using these known values and trigono- A 30° 90° C
metric ratios, they can find the unknown measurement. b
To understand the basis for trigonometry, consider the two triangles in
figure 7.1. Although triangle A'B'C' is larger than triangle ABC, the angles are B'
the same—90, 60, and 30 degrees in this case. Because the angles are the same,
Petroleum Extension-The University of Texas at Austin
the ratios of the sides of the triangles are the same. That is, the length of the 60°
sides of both triangles is proportional to each other because the angles are the c
same. The principles of trigonometry come from these ratios. a
The right triangle (a triangle with a right, or 90-degree, angle) is the basis
for all trigonometry calculations. The relationships between a right triangle’s
angles and sides are simple and well known. Even so, trigonometric formulas A' 30° 90° C '
can also solve problems with oblique triangles, which are triangles without right b
angles, as you will learn later in this chapter. Figure 7.1 Triangle ratios
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