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130 Cards in this Set
- Front
- Back
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Vertical shift up or down?
h(x) = f(x) + c |
Shift up
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Vertical shift up or down?
h(x) = f(x) - c |
Shift down
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Horizontal shift left or right?
h(x) = f(x+c) |
Shift left
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Horizontal shift left or right?
h(x) = f(x-c) |
Shift right
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What kind of reflection?
h(x) = -f(x) |
Reflection on the x axis
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What kind of reflection?
h(x) = f(-x) |
Reflection on the y axis
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y = cf(x); c < 1
Is this a vertical stretch or shrink? |
Vertical Stretch
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y = cf(x); 0 < c < 1
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Vertical Shrink
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Unit Circle:
π/6 |
(√3/2, 1/2)
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Unit Circle
π/4 |
(√2/2, √2/2)
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Unit Circle:
π/3 |
(1/2, √2/2)
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Unit Circle:
π/2 |
(0,1)
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Unit Circle:
2π/3 |
(-1/2, √3/2)
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Unit Circle:
3π/4 |
(-√2/2, √2/2)
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Unit Circle:
5π/6 |
(-√3/2, 1/2)
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Unit Circle:
π |
(-1, 0)
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Unit Circle:
7π/6 |
(-√3/2, -1/2)
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Unit Circle:
5π/4 |
(-√2/2, -√2/2)
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Unit Circle:
4π/3 |
(-1/2, -√3/2)
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Unit Circle:
3π/2 |
(0, -1)
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Unit Circle:
4π/3 |
(-1/2, -√3/2)
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Unit Circle:
3π/2 |
(0, -1)
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Unit Circle:
5π/3 |
(1/2, -√3/2)
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Unit Circle:
7π/4 |
(√2/2, -√2/2)
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Unit Circle:
11π/6 |
(√3/2, -1/2)
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Unit Circle:
2π |
(1, 0)
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Unit Circle:
0 |
(1, 0)
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Unit Circle:
30° |
(√3/2, 1/2)
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Unit Circle:
45° |
(√2/2, √2/2)
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Unit Circle:
60° |
(1/2, √3/2)
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Unit Circle:
90° |
(0, 1)
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Unit Circle:
120° |
(-1/2, √3/2)
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Unit Circle:
135° |
(-√2/2, √2/2)
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Unit Circle:
150° |
(-√3/2, 1/2)
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Unit Circle:
180° |
(-1, 0)
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Unit Circle:
210° |
(-√3/2, -1/2)
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Unit Circle:
225° |
(-√2/2, -√2/2)
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Unit Circle:
240° |
(-1/2, -√3/2)
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Unit Circle:
270° |
(0, -1)
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Unit Circle:
300° |
(1/2, -√3/2)
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Unit Circle:
315° |
(√2/2, -√2/2)
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Unit Circle:
330° |
(√3/2, -1/2)
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Unit Circle:
360° |
(1, 0)
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Find coterminal angle in degrees.
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if angle is positive
angle - 360 = answer angle + 360 = answer if angle is negative 360 - angle = answer -360 - angle = answer |
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Convert degrees to radian
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Angle x (π/180)
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Convert radian to degrees
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Radian x (180/π)
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Find coterminal angle in radians.
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if radian is positive
radian - 2π = answer radian + 2π = answer is radian is negative 2π - radian = answer -2π - radian = answer |
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Unit Circle:
sinθ = |
y
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Unit Circle:
cosθ = |
x
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Unit Circle:
tanθ = |
y/x
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Unit Circle:
cscθ = |
1/y
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Unit Circle:
secθ = |
1/x
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Unit Circle:
cotθ = |
x/y
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Which trigonometric functions are even?
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cosine and secant
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Which trigonometric functions are odd?
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sine, cosecant, tangent, and cotangent
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Right Triangle:
sinθ = |
opp/hyp
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Right Triangle
cosθ = |
adj/hyp
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Right Triangle:
tanθ = |
opp/adj
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Right Triangle:
cscθ = |
hyp/opp
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Right Triangle:
secθ = |
hyp/adj
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Right Triangle:
cotθ = |
adj/opp
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Any Angle:
sinθ = |
y/r
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Any Angle:
cosθ = |
x/r
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Any Angle:
tanθ = |
y/x
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Any Angle:
cscθ = |
r/y
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Any Angle:
secθ = |
r/x
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Any Angle:
cotθ = |
x/y
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Any Angle:
r = |
√(x^2 + y^2)
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Reference Angle:
if 90° < angle < 180° |
180° - Angle
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Reference Angle:
if 180° < angle < 270° |
Angle - 180°
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Reference Angle:
if 270° < angle < 360° |
360 - Angle
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Reference Angle
if π/2 < angle < π |
π - Angle
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Reference Angle:
if π < angle < 3π/2 |
Angle - π
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Reference Angle:
if 3π/2 < angle < 2π |
2π - Angle
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What indicates the amplitude of the following equation?
y = a sin(bx - c) + d |
absolute value of a
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What indicates the amplitude of the following equation?
y = a cos(bx - c) + d |
absolute value of a
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What indicates the period of the following equation?
y = a sin(bx - c) + d |
2π/absolute value of b
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What indicates the period of the following equation?
y = a cos(bx - c) + d |
2π/absolute value of b
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What indicates the horizontal shift of the following equation?
y = a sin(bx - c) + d |
c
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What indicates the horizontal shift of the following equation?
y = a cos (bx - c) + d |
c
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What indicates the line of oscillation of the following equation?
y = a sin (bx - c) + d |
d
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What indicates the line of oscillation of the following equation?
y = a cos (bx - c) + d |
d
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What indicates the period in the following equation?
y = a tan(bx - c) + d |
π/b
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What indicates the asymptote in the following equation?
y = a tan(bx - c) + d |
bx - c = π/2
bx - c = -π/2 |
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What indicates the period of the following equation?
y = a cot (bx - c) + d |
π/2
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What indicates the asymptotes of the following equation?
y = a cot (bx - c) + d |
bx - c = π
bx - c = -π y = 0 |
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Rewrite as inverse
x = sin y |
y = arcsin x
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Rewrite as inverse
x = cos y |
y = cos x
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Rewrite as inverse
x = tan y |
y = arctan x
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What is the standard form for a quadratic equation?
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ax^2 + bx + c
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What is the equation to find the vertex of a quadratic equation?
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(-b/2a, f(x))
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What is the equation to find the axis of symmetry of a quadratic equation?
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-b/2a
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What is the vertex form for a quadratic equation?
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y = a (x - h)^2 + k
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What is the intercept form for a quadratic equation?
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y = a (x - p)(x - q)
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In a polynomial equation, if
f is of an odd degree and the exponent of the leading coefficient > 0, what is the behavior of the graph? |
f(x) →∞ as x →∞
f(x) → - ∞ as x → - ∞ |
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In a polynomial equation if
f is of an odd degree and the exponent of the leading coefficient < 0 what is the behavior of the graph? |
f(x) → - ∞ as x →∞
f(x) →∞ as x → - ∞ |
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In a polynomial equation if
f is of an even degree and the exponent of the leading coefficient is > 0 what is the behavior of the graph? |
f(x) →∞ as x →∞
f(x) → - ∞ as x → - ∞ |
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In a polynomial equation if
f is of an even degree and the exponent of the leading coefficient is < 0 what is the behavior of the graph? |
f(x) → - ∞ as x → ∞
f(x) → - ∞ as x → - ∞ |
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In a rational function, if n < m what is the horizontal asymptote?
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y = 0
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In a rational function, if n = m what is the horizontal asymptote?
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y = a/b
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In a rational function, if n > m what is the horizontal asymptote?
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no horizontal asymptote
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In a rational function, how would you find the vertical asymptote?
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you set the bottom part of the fraction equal to 0 and solve
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In a rational function, how would you find the x intercept?
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Set equation equal to 0 and solve
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In a rational function how would you find the y intercept?
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Replace x with a 0 and solve
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Reciprical Identities:
sin u |
1/ csc u
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Reciprical Identities:
cos u |
1/ sec u
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Reciprical Identities (2):
tan u |
1/ cot u
or sin u/ cos u |
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Reciprical Identities:
csc u |
1/ sin u
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Reciprical Identities:
sec u |
1/ cos u
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Reciprical Identities (2):
cot u |
1/ tan u
or cos u/sin u |
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Pythagorean Identities (3):
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sin^2 u + cos^2 u = 1
1 + tan^2 u = sec^2 u 1 + cot^2 u = csc^2 u |
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sin(π/2 - u)
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cos u
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cos(π/2 - u)
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sin u
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tan(π/2 - u)
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cot u
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cot(π/2 - u)
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tan u
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sec(π/2 - u)
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csc u
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csc(π/2 - u)
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sec u
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Law of Sines
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a/sin a = b/sin b = c/sin c
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Area of an Oblique Triangle
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(1/2)cbsin a
(or any variation of the variables) |
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Law of Cosines (sides)
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a^2 = b^2 + c^2 -2b(cosA)
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Law of Cosines (angles)
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cosA = (b^2 + c^2 - a^2)/2ab
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Heron's Formula (s)
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s = (a+b+c)/2
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Heron's Formula (area)
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area = √s(s-a)(s-b)(s-c)
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Rule for an arithmetic sequence
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an = a1 + (n - 1)(d)
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Sum of a finite arithmetic sequence
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sn = n((a1 + an)/2)
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Rule for the geometric sequence
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an = a1(r)^(n-1)
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Sum of a Finite Geometric sequence
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sn = a1((1-r^n)/(1-r))
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Sum of an infinite geometric sequence
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sn = (a1/(1-r))
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Factor a^3 + b^3
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(a + b)(a^2 – ab + b^2)
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Factor a^3 – b^3
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(a – b)(a^2 + ab + b^2)
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