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Title: Trigonometry Cheat Sheet
Description: Self-created notes! A thorough cheat sheet for trigonometry. Don't let trig get you down again! Valid for all levels of study; A Level, EDEXCEL, etc.
Description: Self-created notes! A thorough cheat sheet for trigonometry. Don't let trig get you down again! Valid for all levels of study; A Level, EDEXCEL, etc.
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Trig Cheat Sheet
Definition of the Trig Functions
Right triangle definition
For this definition we assume that
p
0 < q < or 0° < q < 90°
...
y
( x, y )
hypotenuse
y
opposite
1
q
x
x
q
adjacent
opposite
hypotenuse
adjacent
cos q =
hypotenuse
opposite
tan q =
adjacent
sin q =
hypotenuse
opposite
hypotenuse
sec q =
adjacent
adjacent
cot q =
opposite
csc q =
y
=y
1
x
cos q = = x
1
y
tan q =
x
sin q =
1
y
1
sec q =
x
x
cot q =
y
csc q =
Facts and Properties
Domain
The domain is all the values of q that
can be plugged into the function
...
csc q ³ 1 and csc q £ -1
-1 £ sin q £ 1
-1 £ cos q £ 1 sec q ³ 1 and sec q £ -1
-¥ < tan q < ¥
-¥ < cot q < ¥
Period
The period of a function is the number,
T, such that f (q + T ) = f (q )
...
2p
w
2p
=
w
p
=
w
2p
=
w
2p
=
w
p
=
w
sin ( wq ) ®
T=
cos (wq ) ®
T
tan (wq ) ®
T
csc (wq ) ®
T
sec (wq ) ®
T
cot (wq ) ®
T
© 2005 Paul Dawkins
Formulas and Identities
Tangent and Cotangent Identities
sin q
cos q
tan q =
cot q =
cos q
sin q
Reciprocal Identities
1
1
csc q =
sin q =
sin q
csc q
1
1
sec q =
cos q =
cos q
sec q
1
1
cot q =
tan q =
tan q
cot q
Pythagorean Identities
sin 2 q + cos 2 q = 1
tan 2 q + 1 = sec 2 q
1 + cot 2 q = csc 2 q
Even/Odd Formulas
sin ( -q ) = - sin q
csc ( -q ) = - csc q
cos ( -q ) = cos q
sec ( -q ) = sec q
tan ( -q ) = - tan q
cot ( -q ) = - cot q
Periodic Formulas
If n is an integer
Title: Trigonometry Cheat Sheet
Description: Self-created notes! A thorough cheat sheet for trigonometry. Don't let trig get you down again! Valid for all levels of study; A Level, EDEXCEL, etc.
Description: Self-created notes! A thorough cheat sheet for trigonometry. Don't let trig get you down again! Valid for all levels of study; A Level, EDEXCEL, etc.