tan and arc tan + trig identities galore

arctan(1)

pi/4

arctan(1)

π/4

arctan(0)

0

arctan(-1)

-π/4

arctan(-1)deg

-45

arctan(-Sqrt[3])

-π/3

arctan(Sqrt[3]/3)

π/6

arctan(Sqrt[3])

π/3

arctan(Sqrt[3]/3)

pi/6

tan(pi/6)

Sqrt[3]/3

tan(pi/4)

1

tan(pi/3)

Sqrt[3]

tan(π/2)

undefined

tan(-90)rad

undefined

tan(-pi/6)

-Sqrt[3]/3

tan(-pi/3)

-Sqrt[3]

tan(-pi/2)

undefined

domain of arctan (Degrees)

-90 and 90

domain of arctan(radians)

-π/2 and π/2

sec x

1 / cos x

csc x

1 / sin x

cot x

1 / tan x

tan x

sin x / cos x

cot x

cos x / sin x

cos² x + sin² x

= 1

1 + tan² x

= sec² x

1 + cot² x

= csc² x

sin (2x)

= 2 sin x cos x

cos2x (3)

= cos²x - sin²x

cos² x

= 1/2(1 + cos 2x)

sin² x

= 1/2(1 - cos 2x)

1

sin²A + cos²A

cos²A

1-sin²A

sin²A

1-cos²A

tan

sinx/cosx

cotx

cosx/sinx

cscx

1/sinx

secx

1/cosx

sin2x

2sinxcosx

cos2x (1)

2cos²x-1

cos2x (2)

1-2sin²x

cos2x (3)

cos²x-sin²x

d/dx = e^x

e^x

d/dx secx

tanxsecx

d/dx cscx

-cotxcscx

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

(secx)^2

d/dx cotx

-(cscx)^2

Product Rule

d/dx = vdu/dx + udv/dx

Quotient Rule

d/dx= vdu/dx - u du/dx /v^2

d/dx lnx or logex

1/x

d/dx log base a of (x)

1/(xlna)

d/dx of a^x

a^x lna

d/dx (sin^-1 x)

1/√(1-x^2)

d/dx (cos^-1x)

-1/√(1-x^2)

d/dx (tan^-1x)

1/(1+x^2)

d/dx (cot^-1x)

-1/(1+x^2)

d/dx (sec^-1x)

1/ (|x| √(x^2-1))

d/dx (csc^-1x)

-1/(|x| √(x^2-1))

tan(2π/3)

-√3

tan(3π/4)

-1

tan(5π/6)

-sqrt(3)/3

tan(7π/6)

sqrt(3)/3

tan(5π/4)

1

tan(4π/3)

sqrt(3)

tan(5π/3)

sqrt(3)

tan(7π/4)

-1

tan(11π/6)

sqrt(3)/3

anti dervative of cot

ln|sin(x)| + C

anti derivative of tan(x)

ln|sec x| or -ln|cos x|

anti derivative of sec(x)

ln |sec x + tan x|

anti derivatice of csc x

ln |csc x - cot x|

cot

sec (x)

csc(x)

1/x

1/x²