2.3. TRIGONOMETRIC FUNCTIONS 63
Properties and formulae for trigonometric functions.
Name Abbrev. Value at Domain Range
sine sin opp/hyp .1; 1/ [-1,1]
cosine cos adj/hyp .1; 1/ [-1,1]
tangent tan opp/adj x ¤
2n C 1
2
.1; 1/
cotangent cot adj/opp x ¤ n .1; 1/
secant sec hyp/adj x ¤
2n C 1
2
.1; 1 [ Œ1; 1/
cosecant csc hyp/opp x ¤ n .1; 1 [ Œ1; 1/
Knowledge Box 2.19 shows relationships between the trigonometric functions, many of
them are obvious consequences of the facts in the preceding table. ese are examples of
trigonometric identities.
Knowledge Box 2.19
Some basic identities
For any angle , we have:
• tan./ D
sin./
cos./
• cot./ D
cos./
sin./
• tan./ D
1
cot./
• sec./ D
1
cos./
• csc./ D
1
sin./
2.3.1 GRAPHS OF THE BASIC TRIG FUNCTIONS
Look at the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions in
Figures 2.6–2.8 and check them against the domains and ranges for the functions given earlier
in this section.
e trigonometric functions are periodic, meaning that they repeat their values regularly. is
is visible in their graphs. e sine, cosine, secant, and cosecant functions repeat every 2, while
the tangent and cotangent functions repeat every units.
e functions and co-functions have simple relationships based on sliding the graph sideways.
ese relationships are shown in Knowledge Box 2.20.
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