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Trig Identities
trig review
59
Mathematics
Undergraduate 1
01/09/2008
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Term
sin x
 Definition
o/h
Term
cos x
 Definition
a/h
Term
tan x
 Definition
o/a, sin x/cos x
Term
csc x
 Definition
h/o, 1/sin x
Term
sec x
 Definition
h/a, 1/cos x
Term
cot x
 Definition
a/o, 1/tan x, cos x/sin x
Term
sin x
 Definition
Term
sin^2 x + cos^2 x
 Definition
1
Term
1 + tan^2 x
 Definition
sec^2 x
Term
1 + cot^2 x
 Definition
csc^2 x
Term
sin (pi/2 - x)
 Definition
cos x
Term
cos (pi/2 - x)
 Definition
sin x
Term
csc(pi/2 - x)
 Definition
sec x
Term
tan(pi/2 - x)
 Definition
cot x
Term
sec(pi/2 - x)
 Definition
csc x
Term
cot(pi/2 - x)
 Definition
tan x
Term
sin(-x)
 Definition
-sin x
Term
cos (-x)
 Definition
cos x
Term
csc(-x)
 Definition
-csc x
Term
tan (-x)
 Definition
-tan x
Term
sec (-x)
 Definition
sec x
Term
cot (-x)
 Definition
-cot x
Term
sin(x+-y)
 Definition
sin x cos y +- cos x sin y
Term
cos(u+-v)
 Definition
cos u cos v -+ sin u sin v
Term
tan (u+-v)
 Definition
(tan u +- tan v)/
(1 -+ tan u tan v)
Term
sin 2u
 Definition
2sin u cos u
Term
cos 2u
 Definition
cos^2 u - sin^2 u =
2 cos^2 u - 1 =
1 - 2 sin^2 u
Term
cos^2 u - sin^2 u
 Definition
cos 2u
Term
2 cos^2 u - 1 =
 Definition
cos 2u
Term
1 - 2 sin^2 u
 Definition
cos 2u
Term
tan 2u
 Definition
(2 tan u)/
(1 - tan^2 u)
Term
sin^2 u
 Definition
(1 - cos 2u)/
2
Term
cos^2 u
 Definition
(1 + cos 2u)/
2
Term
tan^2 u
 Definition
(1-cos 2u)/
(1+cos 2u)
Term
sin u + sin v
 Definition
2 sin[(u+v)/2]cos[(u-v)/2]
Term
sin u - sin v
 Definition
2 cos[(u+v)/2]sin[(u-v)/2]
Term
cos u + cos v
 Definition
2 cos[(u+v)/2]cos[(u-v)/2]
Term
cos u - cos v
 Definition
-2sin[(u+v)/2]sin[(u-v)/2]
Term
sin u*sin v
 Definition
1/2[cos(u-v) - cos(u+v)]
Term
cos u*cos v
 Definition
1/2[cos(u-v) + cos(u+v)]
Term
sin u*cos v
 Definition
1/2[sin(u+v) + sin(u-v)]
Term
cos u*sin v
 Definition
1/2[sin(u+v) - sin(u-v)]
Term
cos pi/6
 Definition
√3/2
Term
cos pi/4
 Definition
√2/2
Term
cos pi/3
 Definition
1/2
Term
cos pi/2
 Definition
Term
cos 2pi/3
 Definition
-1/2
Term
cos 3pi/4
 Definition
-√2/2
Term
cos 5pi/6
 Definition
-√3/2
Term
sin pi/6
 Definition
1/2
Term
cos 0
 Definition
1
Term
sin 0
 Definition
Term
sin pi/4
 Definition
√2/2
Term
sin pi/3
 Definition
√3/2
Term
sin pi/2
 Definition
1
Term
sin 3pi/4
 Definition
√2/2
Term
sin 5pi/6
 Definition
1/2
Term
2 sin u cos u
 Definition
sin 2u
Term
(2 tan u)/
(1 - tan^2 u)
 Definition
tan 2u
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