Begin2.DVI

Powers of trigonometric functions

sin^2 A=

1

2 −

1

2 cos 2A,

sin^3 A=^3

4

sinA−^1

4

sin 3A,

sin^4 A=^3

8

−^1

2

cos 2A+^1

8

cos 4A,

cos^2 A=

1

2 +

1

2 cos 2A

cos^3 A=^3

4

cosA+^1

4

cos 3A

cos^4 A=^3

8

+^1

2

cos 2A+^1

8

cos 4A

Inverse Trigonometric Functions

sin−^1 x=π 2 −cos−^1 x

cos−^1 x=π 2 −sin−^1 x

tan−^1 x=π 2 −cot−^1 x

sin−^1

1

x= csc

− (^1) x
cos−^11
x
= sec−^1 x
tan−^1
1
x= cot
− (^1) x
Symmetry properties of trigonometric functions
sinθ=−sin(−θ) = cos(π/ 2 −θ) =−cos(π/2 +θ) = + sin(π−θ) =−sin(π+θ)
cosθ= + cos(−θ) = sin(π/ 2 −θ) = + sin(π/2 +θ) =−cos(π−θ) =−cos(π+θ)
tanθ=−tan(−θ) = cot(π/ 2 −θ) =−cot(π/2 +θ) =−tan(π−θ) = + tan(π+θ)
cotθ=−cot(−θ) = tan(π/ 2 −θ) =−tan(π/2 +θ) =−cot(π−θ) = + cot(π+θ)
secθ= + sec(−θ) = csc(π/ 2 −θ) = + csc(π/2 +θ) =−sec(π−θ) =−sec(π+θ)
cscθ=−csc(−θ) = sec(π/ 2 −θ) = + sec(π/2 +θ) = + csc(π−θ) =−csc(π+θ)
Transformations
The following transformations are sometimes useful in simplifying expressions.

1. Iftanu
   2

=A, then

sinu=

2 A

1 +A^2 , cosu=

1 −A^2

1 +A^2 , tanu=

2 A

1 −A^2

2. The transformationsinv=y, requirescosv=

√
1 −y^2 , andtanv=√ y
1 −y^2
Law of sines

a

sinA

= b

sinB

= c

sinC

Law of cosines

a^2 =b^2 +c^2 − 2 bccosA

b^2 =c^2 +a^2 − 2 accosB

c^2 =a^2 +b^2 − 2 abcosC