Trigonometric Functions of a General Angle in .NET

Print QR Code JIS X 0510 in .NET Trigonometric Functions of a General Angle

CHAPTER 2 Trigonometric Functions of a General Angle
Decode QR In Visual Studio .NET
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET applications.
QR Code 2d Barcode Creation In .NET Framework
Using Barcode generator for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in .NET applications.
Fig. 2.8
Read QR Code JIS X 0510 In .NET
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
Barcode Creator In .NET Framework
Using Barcode maker for VS .NET Control to generate, create bar code image in Visual Studio .NET applications.
For any angle , cos x/r and sin y/r. On a unit circle, r 1 and the arc length s r and cos cos s x/1 x and sin sin s y/1 y. The point P associated with the arc length s is determined by P(x, y) P(cos s, sin s). The wrapping function W maps real numbers s onto points P of the unit circle denoted by W(s) (cos s, sin s)
Bar Code Reader In VS .NET
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
QR Code ISO/IEC18004 Generation In C#.NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR-Code image in Visual Studio .NET applications.
Some arc lengths are paired with points on the unit circle whose coordinates are easily determined. If s 0, the point is (1, 0); for s /2, one-fourth the way around the unit circle, the point is (0, 1); s is paired with ( 1, 0); and s 3 /2 is paired with (0, 1). (See Sec. 1.5.) These values are summarized in the following chart.
Making QR Code In Visual Studio .NET
Using Barcode maker for ASP.NET Control to generate, create QR-Code image in ASP.NET applications.
Creating QR In Visual Basic .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR image in .NET framework applications.
s 0 /2 P(x, y) (1, 0) (0, 1) ( 1, 0) 3 /2 (0, 1) cos s 1 0 1 0 sin s 0 1 0 1
Linear 1D Barcode Generation In .NET
Using Barcode maker for VS .NET Control to generate, create Linear Barcode image in VS .NET applications.
Generate Barcode In Visual Studio .NET
Using Barcode generation for Visual Studio .NET Control to generate, create barcode image in .NET framework applications.
Circular Functions
Encoding 2D Barcode In Visual Studio .NET
Using Barcode drawer for .NET Control to generate, create Matrix Barcode image in .NET framework applications.
Print USPS PLANET Barcode In .NET Framework
Using Barcode creator for .NET Control to generate, create Planet image in Visual Studio .NET applications.
Each arc length s determines a single ordered pair (cos s, sin s) on a unit circle. Both s and cos s are real numbers and define a function (s, cos s) which is called the circular function cosine. Likewise, s and sin s are real numbers and define a function (s, sin s) which is called the circular function sine. These functions are called circular functions since both cos s and sin s are coordinates on a unit circle. The circular functions sin s and cos s are similar to the trigonometric functions sin u and cos u in all regards, since, as shown in Chap. 1, any angle in degree measure can be converted to radian measure, and this radian-measure angle is paired with an arc s on the unit circle. The important distinction for circular functions is that since (s, cos s) and (s, sin s) are ordered pairs of real numbers, all properties and procedures for functions of real numbers apply to circular functions. The remaining circular functions are defined in terms of cos s and sin s. tan s cot s sec s csc s sin s cos s cos s sin s 1 cos s 1 sin s for s 2 p 2 kp where k is an integer
Drawing Universal Product Code Version A In VB.NET
Using Barcode maker for VS .NET Control to generate, create GTIN - 12 image in Visual Studio .NET applications.
Create ANSI/AIM Code 39 In Java
Using Barcode generation for Android Control to generate, create Code 39 Extended image in Android applications.
for s 2 kp where k is an integer for s 2 p 2 kp where k is an integer
UPC Code Generator In Java
Using Barcode creator for Eclipse BIRT Control to generate, create UPC Code image in BIRT reports applications.
Code-128 Creator In Visual Studio .NET
Using Barcode printer for ASP.NET Control to generate, create Code 128 image in ASP.NET applications.
for s 2 kp where k is an integer
Generating GS1-128 In None
Using Barcode printer for Excel Control to generate, create USS-128 image in Excel applications.
Create Data Matrix 2d Barcode In VS .NET
Using Barcode creator for ASP.NET Control to generate, create Data Matrix 2d barcode image in ASP.NET applications.
CHAPTER 2 Trigonometric Functions of a General Angle
Draw Code 128B In Java
Using Barcode maker for Java Control to generate, create Code-128 image in Java applications.
Draw EAN 13 In Java
Using Barcode generator for Android Control to generate, create GS1 - 13 image in Android applications.
It should be noted that the circular functions are defined everywhere that the trigonometric functions are defined, and the values left out of the domains correspond to values where the trigonometric functions are undefined. In any application, there is no need to distinguish between trigonometric functions of angles in radian measure and circular functions of real numbers.
SOLVED PROBLEMS
2.1 Using a rectangular coordinate system, locate the following points and find the value of r for each: A(1, 2), B( 3, 4), C( 3, 3 23), D(4, 5) (see Fig. 2.9).
For A: r For B: r For C: r For D: r 2x2 29 29 216 y2 16 27 25 21 5 6 241 4 25
Fig. 2.9
2.2 Determine the missing coordinate of P in each of the following: (a) (b) (c) (d) x x y x 2, r 3, P in the first quadrant 3, r 5, P in the second quadrant 1, r 3, P in the third quadrant 2, r 25, P in the fourth quadrant (e) (f) (g) (h) x y x y 3, r 3 2, r 2 0, r 2, y positive 0, r 1, x negative
5 and y 25. 4. 2 22. 1. 0. 25.
(a) Using the relation x2 y2 r2, we have 4 y2 9; then y2 Since P is in the first quadrant, the missing coordinate is y (b) Here 9 y2 25, y2 16, and y 4. Since P is in the second quadrant, the missing coordinate is y (c) We have x 1 9, x 8, and x 2 22. Since P is in the third quadrant, the missing coordinate is x
(d) y
4 and y r
1. Since P is in the fourth quadrant, the missing coordinate is y 9 9 0. 0 and the missing coordinate is y
Copyright © OnBarcode.com . All rights reserved.