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Trigonometric Identities
Handy Trigonometric identities for precalculus
31
Mathematics
11th Grade
11/04/2010
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Term
sin n =
 Definition
(y/r)
Term
cos n =
 Definition
(x/r)
Term
sin 45 =
 Definition
(2^(1/2))/2
Term
cos 45 =
 Definition
(2^(1/2))/2
Term
sin 60 =
 Definition
(3^(1/3))/2
Term
cos 30 =
 Definition
(3^(1/3))/2
Term
sin 30 =
 Definition
(1/2)
Term
cos 60 =
 Definition
(1/2)
Term
csc n =
 Definition
(1/sin n) = (r/y)
Term
sec n =
 Definition
(1/cos n) = (r/x)
Term
cot n =
 Definition
(1/tan n) = (x/y) = (cos n / sin n)
Term
tan n =
 Definition
(sin n/ cos n)
Term
(cos n)^2 =
 Definition
1 - (sin n)^2
Term
(sin n)^2 =
 Definition
1 - (cos n)^2
Term
(sec n)^2 =
 Definition
1 + (tan n)^2
Term
(tan n)^2 =
 Definition
(sec n)^2 - 1
Term
Law of Sines
 Definition
((sin A)/a) = ((sin B)/b) = ((sin C)/c)
Term
Law of Cosines
 Definition
c^2 = a^2 + b^2 -2ab(cos C)
Term
sin 2n =
 Definition
2(sin n)(cos n)
Term
cos 2n =
 Definition
(cos n)^2 - (sin n)^2 = 1 - 2((sin n)^2) = 2((cos n)^2) - 1
Term
tan 2n =
 Definition
(2(tan n))/(1 - (tan n)^2)
Term
(sec n)^2 + (csc n)^2 =
 Definition
((sec n)^2)((csc n)^2)
Term
((sec n)^2)((csc n)^2) =
 Definition
(sec n)^2 + (csc n)^2
Term
cos (A - B) =
 Definition
(cos A)(cos B) + (sin A)(sin B)
Term
cos (A + B) =
 Definition
(cos A)(cos B) - (sin A)(sin B)
Term
sin (A - B) =
 Definition
cos ((90 - A) - B) = (sin A)(cos B) - (cos A)(sin B)
Term
sin (A + B) =
 Definition
(sin A)(cos B) + (cos A)(sin B)
Term
x =
 Definition
r(cos n)
Term
y =
 Definition
r(sin n)
Term
Euler's Formula
 Definition
e^((n)(i)) = cos n + i(sin n)
r(e^((n)(i))) = r(cos n + i(sin n))
Term
cis n =
 Definition
cos n + i(sin n)
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