Attacking Trigonometry Problems

David S. Kahn

• Publisher: Dover Publications
• Year: 2015
• ISBN:
  9780486804798
• Topic: Matematica
• Subtopic: Trigonometria

This volume offers a concise, highly focused review of what high school and beginning college undergraduates need to know to successfully solve the trigonometry problems they will encounter on exams. Rigorously tested examples and coherent, to-the-point explanations are presented in an accessible form and will provide valuable assistance in conquering this challenging subject.
Rather than serving as a text or treatise, the book focuses on the essentials of trigonometry. All fourteen sections are organized in a manner that allows readers to advance sequentially or to skip around. The approach encourages memorization of ratios and formulas, and the practice problems offer ample opportunities to become comfortable with applying the trig ratios to a variety of settings.

UNIT SIX

Some Basic Trigonometry Problems

So far, we have learned all six trig ratios – sine, cosine, tangent, cotangent, secant, and cosecant – and we have learned how to find their values at a variety of angles. But, all of the angles that we have used so far have been the special angles. Now, we will learn how to find the trig ratios for any angle.

If you want to find the trig ratio of an angle, you simply use your calculator. For example, if you want to find sin 37^°, you plug sin 37^° into your calculator. You should get approximately 0.6018. There are two very important things to keep in mind when using your calculator for trigonometry.

First, calculators will give you the choice of two modes – degrees or radians. (A few calculators also offer grads, but we will not work with grads in this book.) So, when you evaluate the trig ratio of an angle, make sure that you are in the correct mode! An easy way to check is to enter sin 30^° on your calculator. If you are in Degree Mode, you will get 0.5. If you don’t, then the calculator is in Radian Mode. Be careful! Many students mess up on exams by having their calculators in the wrong mode.

Second, when a calculator gives you the value of a trig function of an angle, it is giving you a decimal approximation. It is traditional to round to 4 decimal places, although you can feel free to use as many as you wish. Just keep in mind that your answer will be an approximation, not an exact value, unless you are finding the trig ratio of one of the special angles.

One type of problem that you will be asked to solve is, given an angle and a side of a triangle, find one of the other sides.

Example 1: In the right triangle ABC below, ∠C is the right angle and ∠A = 40^°. If AB = 12, how long is BC?

Figure 1

Given AB, the hypotenuse of the triangle, we ...