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Door Trig

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Submitted By beez
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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° .
2

Unit circle definition
For this definition q is any angle. 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. sin q , q can be any angle cos q , q can be any angle

æ tan q , q ¹ ç n + ÷ p , n = 0, ± 1, ± 2,K

è csc q , q ¹ n p , n = 0, ± 1, ± 2,K

æ sec q , q ¹ ç n + ÷ p , n = 0, ± 1, ± 2,K

è cot q , q ¹ n p , n = 0, ± 1, ± 2,K

Range
The range is all possible values to get out of 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 ) . So, if w is a fixed number and q is any angle we have the following periods.
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

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