Download 2,3,7,8,13,14,17,19,26,27,29,31,34,38,41a-c,43,44,54

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.