Trig Identities/Parametric

csc (x)

1/sin(x)

sec(x)

1/cos(x)

cot(x)

1/tan(x)

sin² (x)+cos² (x)

1

sec² (x)

1+tan² (x)

csc² (x)

1+cot² (x)

as x approaches 0, sin (x)/x

1

1st derivative

dy/dt / dx/dt

2nd derivative

dy ‘/dt / dx/dt

Speed

sqrt (dx/dt)²+(dy/dt)²h

1/∞

0

ln (0)

-∞

1/0

∞

anything over 0 is…

undefined

∞ multiplied by ∞

∞

inverse of sin x/arcsin

1/√1-x²

inverse of cos x/ arccos

-1/√1-x²

inverse tanx/ arctan

1/1+x²

inverse cotx/arccot

-1/1+x²

inverse secx/ arcsec

1/x√x2-1

inverse cscx/arccsc

-1/x√x2-1

Area of semicircle

pi(r²)/2

Area of quarter circle

pi(r²)/4

f(x) is odd

integral of -a to a of f(x)= 0

f(x) is even

integral of -a to a is 2 of f(x) is 2 times integral 0 to a f(x)

integral of 5^x

5^x/ln(5) + C

sin(x) integral

-cos(x)

integral cos(x)

sin(x)

sec²(x)

tan(x)+C

csc²(x)

-cot(x)+C

csc(x)cot(x)

-csc(x)+C