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13-8 RECIPROCAL TRIGONOMETRIC FUNCTIONS (p. 749-755) The cosecant (csc), secant (sec), and cotangent (cot) functions are reciprocals of the three functions that we have studied to this point- sin, cos, and tan, respectively. Their domains include all real numbers except those that make a denominator zero. 1 1. csc sin 1 2. sec cos 1 3. cot tan By using the above definitions, you can evaluate these reciprocal trigonometric functions. Example: Find the following. Round to the nearest hundredth. 1. csc 45 4 2. Suppose cos . Find sec . 5 Do 1 a and b on p. 749. You can use what you know about special right triangles (30-60-90 and 45-45-90) and the unit circle to find exact values for reciprocal trigonometric functions. Example: Find the exact value of csc 45. Sketch a 45 angle in standard position and the unit circle. Use a 45-45-90 triangle. Do 2a-c on p. 750. You can also evaluate these reciprocal functions in radians. Example: Use your TI in radian mode to evaluate each expression. Round to the nearest thousandth. 1. cot ( ) 5 2. sec (-2) Do 3 a-c on p. 750. The graphs of the reciprocal trigonometric functions have asymptotes (they are undefined) where their denominators are zero. Example: Sketch y cos x and y sec x in the interval from 0 to 2 . Make a table of values as in Ex. 4 on p. 751 (perhaps evaluate at every rather than ). Use the TI and 6 4 round values to the nearest tenth. Note that y sec x will have a vertical asymptote wherever cos x 0. Do 4 on p. 751. You can also use the TI to quickly graph reciprocal trigonometric functions. Example: Graph y sec x on the TI. Find the sec 13 . Do 5 on p. 751. Examine and discuss Ex. 6 on p. 752. There are errors in my book and even in the students’ book. Do 6 on p. 752. These relationships are not mentioned in this section, but they are beneficial to know. sin 1. tan cos cos 2. cot sin Example: Find cot 60 . Homework p. 752-753: 2,3,7,8,13,14,17,19,26,27,29,31,34,38,41a-c,43,44,54-56,70,86 54a. y csc x domain: all real numbers except multiples of range: all real numbers 1 or -1 period: 2 b. 1 c. –1 55a. Reciprocals have the same sign. b. The reciprocal of –1 is –1.