March 2011
Intermediate to advanced
829 pages
25h 44m
English
Content preview from Technical Mathematics, Sixth Edition
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
8.1. Trigonometric Functions of Any Angle
In Chap. 7 we defined the sine, cosine, and tangent of acute angles. We did this in terms of the sides of a right triangle, and also for an angle in standard position. Let us now expand this definition to angles of any size.
We also introduce three new trigonometric functions, the cotangent, secant, and cosecant. Their definitions, along with the sine, cosine, and tangent, are
Figure 8-3 shows angles in the second, third, and fourth quadrants. The trigonometric functions of any of these angles are defined exactly as for an acute angle in quadrant I. From any point P on the terminal side of the angle we drop a perpendicular to the x axis, forming a right triangle with legs x and y and with a hypotenuse r. The six trigonometric functions are then given by Eqs. 111 through 113, just as before, except that some of the functions are now negative.
Figure 8.3. FIGURE 8-3
Example 1:A point on the terminal side of angle θ has the coordinates (−3, −5). Write the six trigonometric functions of θ to three significant digits. Solution: We sketch the angle as shown in Fig. 8-4 and see that it lies in the third quadrant. We find distance r by the Pythagorean theorem. Then, |
Figure 8.4. FIGURE 8-4
8.1.1. Trigonometric Functions of Any Angle by ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.