Chapter 8. Oblique Triangles and Vectors

OBJECTIVES

When you have completed this chapter, you should be able to

  • Write the trig function of any angle given a point on the terminal side.

  • Find a trig function for any angle using a calculator.

  • Identify the algebraic sign of a given trig function for any angle in any quadrant.

  • Determine the reference angle for a given angle.

  • Determine the angle(s), given the value of a trig function.

  • Solve oblique triangles using the law of sines.

  • Solve oblique triangles using the law of cosines.

  • Solve applied problems involving oblique triangles.

  • Find the resultant of vectors at any angle.

  • Determine the resultant of any number of vectors.

  • Resolve any vector into its components.

  • Solve applied problems involving vectors.

In the preceding chapter we learned just enough trigonometry to solve right triangles. Even with those few tools you saw that we were able to handle a great variety of applications, including vectors at right angles.

However, many applications require us to solve an oblique triangle, such as for finding distance PQ in Fig. 8-1. For these, we need to be able to write the trigonometric functions of an obtuse angle. Further, two vectors are not always perpendicular but can be at any angle, such as the force vectors in Fig. 8-2. For such applications we need to be able to write the trigonometric functions of any angle, including those greater than 180°.

To start, we will expand our definition of the trigonometric functions to include angles in any ...

Get Technical Mathematics, Sixth Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial