Precalc Midterm!!!
vertical stretch=
#>1f(x)
equation of a circle=
(x-h)²+ (y-k)²=r²
equation of a horizontal ellipse=
(x-h)²/a² + (y-k)²/b²=1
horizontal hyperbola equation=
(x-h)²/a² - (y-k)²/b²=1
equation of a vertical ellipse=
(x-h)²/b² + (y-k)²/a²=1
reflection over x-axis=
-f(x)
area of a non-right triangle equation=
1/2absinθ
what is the frequency equation/how do you find the period in cos and sin functions?
2π/B
how many critical points do you need?
5
vertical compression=
fraction/decimalf(x)
in y=atrigB(A-C)+D, what is B?
frequency
what is the +cos pattern?
max, mid, min, mid, max
what is the +sin pattern?
mid, max, mid, min, mid
what is the -sin pattern?
mid, min, mid, max, min
what is the -cos pattern?
min, mid, max, mid, min
n y=atrigB(A-C)+D, what is C?
phase shift
parametric for sec and tan=
sec(t)²- tan(t)²=1
in the equation y= 2/x-1 +4, what is '2'?
vertical shift
in y=atrigB(A-C)+D, what is D?
vertical shift
the amplitude will show the what?
vertical stretch/compression
in y=atrigB(A-C)+D, what is A?
x
it's a horizontal hyperbola when the ___ is first/positve
x value
it's a horizontal ellipse when the ____is bigger in the denominator
x/a² value
horizontal parabola formula=
x=a(y-k)²+h
parametric form of a circle=
x=rcos(t)+h, y=rsin(t)+k
projectile motion equation for x=
x=tvcosθ
it's a vertical hyperbola when the ___ is first/positive
y value
it's a vertical ellipse when the ____ is bigger in the denominator=
y/b² value
projectile motion equation for y=
y= -1/2gt²+tvsinθ+h
vertical parabola formula=
y=a(x-h)²+k
graphing trig function equation=
y=atrigB(A-C)+D
if you square root something, the new value will have a ? in front of it?
±
what is the frequency equation/how do you find the period in tan functions?
±π÷2/B
how to find the foci in a hyperbola=
c²=a²+b²
law of cosine formula
c²=a²+b²-2ab*cos(C)
focal point equation=
c²=a²-b²
horizontal compression=
f(#>1x)
reflection over y-axis=
f(-x)
horizontal stretch=
f(fraction/decimalx)
major axis =2 times...
a
in ellipses/hyperbolas, the bottom value of the fraction is your _____ value squared=
a/b
how to find focal point of a parabola=
a=1/4c
minor axis=2 times....
b
parametic sin and cos=
cos(t)² + sin(t)²=1
