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arcsin restriction of range

[-π/2, π/2]

arccos restriction of range

[0, π]

arctan restriction of range

(-π/2, π/2)

arccsc restriction of range

[-π/2, π/2] except 0

arcsec restriction of range

[-π/2, π/2] except 0

arccot restriction of range

[-π/2, π/2] except π/2

y=tanx vs. y=cotx

The functions y=tanx and y=cotx are reciprocal trigonometric functions; tanx is defined for all real numbers except odd multiples of π/2, while cotx is defined for all real numbers except integer multiples of π.

formula to convert radians to degrees

radians/π = degrees/180

half angle identity → cos²x=

cos²x = ½ + ½ cos (2x)

half angle identity → sin²x=

sin²x = ½ - ½ cos (2x)

double angle identity → cos2u =

cos 2u = cos²u - sin²u = -2sin²u+1 = 2cos²u-1

double angle identity → sin 2u =

sin 2u = 2 sinu - cosu

double angle identity → tan 2u =

(2 tan u)/(1-tan²u)

compound angle identity → sin (x±y) =

sin x cos y ± cos x sin y

cos (x±y) =

cos x cos y ∓ sin x sin y

tan (x±y)=

tan x ± tan y / 1 ∓ tan x tan y

terminal side

side that determines the angle

coterminal angles

angles that have same terminal side (210° and -150°)

period formula

2π/b = period

y=sin(1/2x) would stretch by ___

scale factor of 2

sin²x+cos²x=?

1

sin(90°-x) =

cos x