9c)++Trig+functions+of+any+angle

If you have used sine, cosine, and tangent only to figure out the sides and angles of a right triangle, then you probably haven't considered taking sin(230°) or tan(-30°). In this section, we will treat the trig ratios (sin, cos, tan, sec, csc, cot) as functions, and the domains of each of them will be expanded beyond the interval (0°, 90°). The domains of sin(x) and cos (x) are all real numbers, and the domains of the other four will also extend from negative to positive infinity, with some values where these functions are undefined.

In this section, we will show how to take trig functions of any angle. You will need to understand the meaning of all six trig functions, not just sin, cos, and tan, so make sure you know the topics of Section 9a) of this review guide. You will also need to be able to use //reference angles// and //coterminal angles//, which are in Section 9b) of this guide. Finally, you will also need to remember the side ratios of the //special right triangles// that you learned in Geometry last year. You know, those are the 45-45-90 and 30-60-90 triangles whose sides always have specific ratios, as shown below: Our textbook teaches this topic in primarily in sections 13-3 and 13-4, with a little bit in section 13-2.

If you need help on this topic, you can view the following **Tutorial** or look at the websites linked below.

Here are two **websites** that will help you take trig functions of any angle: [|Trig without tears (http://oakroadsystems.com/twt/refangle.htm#refangleTop)] [|Interactive Math (http://www.intmath.com/Trigonometric-functions/5_Signs-of-trigonometric-functions.php)]

Want to try out your skills? Try these problems: Problem 1: a) tan 335° = -0.446 . Find another angle between 0° and 360° that has the same value for tan. b) sin 48° = 0.743. Find another angle between 0° and 360° that has the same value for sin. c) cos (–70°) = 0.342 . Find two angles between 0° and 360° that have this value for cos.

Problem 2: Find the following trig functions without a calculator: Problem 3: Find all of the angles that satisfy Problem 4:

__Answers__: Problem 1: a) 155º b) 132º c) 70º and 290º Problem 2: Problem 3:  Problem 4:

Here are worked-out solutions to the problems in this section: