Functions Flashcards
What does [ mean?
the number can go up to and include
What does ( mean?
the number can go up to but not include it
What is an even function?
f(-x) = f(x)
What does an even function look like?
What is an odd function?
f(-x) = -f(x)
What does an odd function look like?
What is a periodic function?
f(t + nT)
y = f(t) if there is a number T, such that f(t + nT) = f(t), all integers n then f(t) is periodic.
What does a continuous function look like?
What does a discontinuous function look like?
What does a discontinuous function look like?
How do you convert from degrees to radians?
x pi/180
How do you convert from radians to degrees?
x 180/pi
what period does y = cosθ have?
2*pi
Is y = cosθ an ODD, EVEN or neither function?
Even
What period does y = sinθ have?
2*pi
What function is y = sinθ EVEN, ODD or neither?
Odd
What period does y = tanθ have?
2*pi
What period does y = tanθ have?
2*pi
What function does y = tanθ EVEN, ODD or neither?
ODD
What is the identity that includes cos^2(θ) and sin^2(θ)?
cos^2(θ) + sin^2(θ) = 1
What does cos(a + b) =
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
What does cos(a + b) =
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
What does cos(a - b) =
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
What does sin(a + b) =
sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
what does sin(a - b) =
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
what is the equation for binomial expansion?
what is the equation for the generalised binomial coefficients?
given f, find f^(-1)?
put y = f(x)
solve for x
find the inverse function for y = sinθ?
find the inverse function for y = sinθ?
find the inverse function for y = sinθ?
What does the graph for y = arccosθ look like?
What does the graph for y = arccosθ look like?
What does the graph for y = arctanθ look like?
what does e^x differentiate to?
e^x
What does the graph e^x look like?
What does the graph y = ln(x) look like?
ln(e^x) =
x
e^ln(x) =
x
ln(xy) =
ln(xy) = ln(x) + ln(y)
ln(x/y) =
ln(x/y) = ln(x) - ln(y)
ln(x^p) =
p*ln(x)
what does ln(x) differentiate to?
1/x
a^x = y <=>
log_a(y)
What is sinh(x) =
sinh(x) = 1/2*(e^x - e^(-x))
What is cosh(x)?
cosh(x) = 1/2*(e^x + e^(-x))
What is tanh(x)?
tanh(x) = sinh(x)/cosh(x)
What does the graph for sinh(x) look like?
What does the graph for cosh(x) look like?
What does the graph for tanh(x) look like?
What is the identity that links cosh(x) and sinh(x)?
cosh^2(x) - sinh^2(x) = 1
what does cosh(a + b) =
cosh(a + b) = cosh(a)cosh(b) + sinh(a)sinh(b)
What does cosh(2x) =
cosh(2x) = cosh^2(x) + sinh^2(x)
what does sinh(a + b) =
sinh(a + b) = cosh(a)sinh(b) + sinh(a)cosh(b)
what does sinh(2x) =
sinh(2x) = 2sinh(x)cosh(x)
what does sinh(x) differentiate into?
cosh(x)
What does cosh(x) differentiate into?
sinh(x)
