TRIGONOMETRY

[Pages:1]Right Triangle Definitions

sin = opp cos = adj

hyp

hyp

tan = opp cot = adj

adj

opp

sec = hyp csc = hyp

adj

opp

TRIGONOMETRY

Circular Definitions

sin = y r

tan = y x

cos = x r

cot = x y

sec = r csc = r

x

y

Other Identities

tan x = sin x cos x

sec x = 1 cos x

cot x = cos x sin x

csc x = 1 sin x

Reduction Formulas sin(-x) = - sin(x) cos(-x) = cos(x) tan(-x) = - tan(x) cot(-x) = - cot(x) sec(-x) = sec(x) csc(-x) = - csc(x)

Sum and Difference Formulas cos(u ? v) = cos u cos v sin u sin v sin(u ? v) = sin u cos v ? cos u sin v

tan u ? tan v tan(u ? v) =

1 tan u tan v

Pythagorean Identities sin2 + cos2 = 1 1 + tan2 = sec2 1 + cot2 = csc2

Double Angle Formulas sin(2u) = 2 sin u cos u cos(2u) = cos2 u - sin2 u cos(2u) = 2 cos2 u - 1 cos(2u) = 1 - 2 sin2 u

2 tan u tan(2u) = 1 - tan2 u

Power Reducing Formulas

sin2 u = 1 - cos(2u) 2

cos2 u = 1 + cos(2u) 2

tan2 u = 1 - cos(2u) 1 + cos(2u)

Cofunction Identities

sin

2

-

x

=

cos

x

tan

2

-

x

=

cot

x

sec 2

-

x

=

csc

x

cos

2

-

x

=

sin

x

cot

2

-

x

=

tan

x

csc

2

-

x

=

sec

x

Product to Sum Formulas sin u sin v = 0.5[cos(u - v) - cos(u + v)] cos u cos v = 0.5[cos(u - v) + cos(u + v)] sin u cos v = 0.5[sin(u + v) + sin(u - v)] cos u sin v = 0.5[sin(u + v) - sin(u - v)]

Special Angles

3 cos 0 = 1 cos =

62

sin 0 = 0

sin

=

1

62

2 cos =

42

sin =

2

42

1 cos =

32

sin =

3

32

cos = 0

2

sin = 1

2

d sin x = cos x

dx

d tan x = sec2 x dx

d sec x = sec x tan x

dx

d cos x = - sin x

dx

d cot x = - csc2 x dx

d csc x = - csc x cot x

dx

Derivative Rules

d

1

arcsin x =

dx

1- x2

d

1

dx arctan x = x2 + 1

d

1

arc sec x =

dx

x x2 -1

d ln x = 1

dx

x

d cosh x = sinh x dx

d sinh x = cosh x

dx

d a x = ln a a x dx

d xn = n xn-1 dx

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