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Algebra II & Trigonometry
A2.A.55
A2.A.59
A2.A.62
Date _____________________________________
Reciprocal Trig Functions
Express and apply the six trigonometric functions as ratios of the sides of a right triangle
Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent
of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
Find the value of trigonometric functions, if given a point on the terminal side of angle 
In 1 – 12, write each expression in terms of sin , cos , or both. Simplify wherever possible.
1. tan 
2. cot 
3. sec 
4. csc 
7.
10.
5. tan   csc 
tan 
sec
8.
tan 
cot
11.
cos
sec
sec
cot
6.
cot
csc
9.
sin
csc
12.
sec
csc
In questions 13 – 18, use the triangle below to find the trigonometric value from the question.
13. sin A
14. csc A
15. cot A
16. sec A
17. tan A
18. cos A
19. If x is the measure of an angle in standard position and its terminal side passes through the point (–5, 12), find the
exact value of:
(a) cos x
(b) sin x
(c) tan x
(d) sec x
(e) csc x
In 20 – 27, find the exact numerical value of each expression.
20. csc 150
21. sec 240
24. sec 2
23. csc 120
26. csc
22. cot 315
3
2
27. sec
25. cot

6
5
4
28. If  is an angle in standard position and its terminal side passes through the point (4, 3), find:
(a) cot 
(b) tan 
(c) cos 
(d) csc 
(e) sec 
29. Given that A is an angle in standard position and the terminal side of angle A passes through the point (5, –2), what
is the exact value of:
(a) sin 
(b) tan 
(c) cos 
(d) csc 
(e) sec 
19. Copy and complete the following table into your homework notebook. If a function is undefined for an angle
measure, write “undefined.”

sin 
cos 
tan 
sec 
csc 
cot 
0
30
45
60
90`