538 CHAPTER 5 Trigonometric Functions (b) Figure 21 shows the angle. Here, x = -3, y = 0, and r = 3, so the trigonometric functions have the following values. sin u = 0 3 = 0 cos u = -3 3 = -1 tan u = 0 -3 = 0 csc u = 3 0 Undefined sec u = 3 -3 = -1 cot u = -3 0 Undefined Verify that these values can also be found using the point 1-1, 02. S Now Try Exercises 21, 55, 57, and 59. x y 0 (–3, 0) u Figure 21 The conditions under which the trigonometric function values of quadrantal angles are undefined are summarized here. Conditions for Undefined Function Values Identify the terminal side of a quadrantal angle. • If the terminal side of the quadrantal angle lies along the y-axis, then the tangent and secant functions are undefined. • If the terminal side of the quadrantal angle lies along the x-axis, then the cotangent and cosecant functions are undefined. The function values of some commonly used quadrantal angles, 0°, 90°, 180°, 270°, and 360°, are summarized in the table. They can be determined when needed using Figure 19 on the previous page and the method of Example 4(a). For other quadrantal angles such as -90°, -270°, and 450°, first determine the coterminal angle that lies between 0° and 360°, and then refer to the table entries for that particular angle. For example, the function values of a -90° angle would correspond to those of a 270° angle. Function Values of Quadrantal Angles U sin U cos U tan U cot U sec U csc U 0° 0 1 0 Undefined 1 Undefined 90° 1 0 Undefined 0 Undefined 1 180° 0 -1 0 Undefined -1 Undefined 270° -1 0 Undefined 0 Undefined -1 360° 0 1 0 Undefined 1 Undefined The values given in this table can be found with a calculator that has trigonometric function keys. Make sure the calculator is set to degree mode. TI-84 Plus Figure 22 CAUTION One of the most common errors involving calculators in trigonometry occurs when the calculator is set for radian measure, rather than degree measure. Be sure to set your calculator to degree mode. See Figure 22.
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