Download Right Triangle: sin θ opp hyp Right Triangle: cos θ adj hyp Right

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Right Triangle:
sin θ
opp
hyp
Right Triangle:
cos θ
adj
hyp
Right Triangle:
tan θ
Circular function, radius r
sin θ
Circular function, radius r
cos θ
opp
adj
y
r
x
r
2
Circular function, radius r
tan θ
Reciprocal Identity:
csc θ
Reciprocal Identity:
sec θ
Reciprocal Identity:
cot θ
Reciprocal Identity:
1
y
x
1
sin θ
1
cos θ
1
tan θ
sin x csc x
or
cos x sec x
or
tan x cot x
3
Pythagorean Identities:
sin 2 x + cos 2 x =
1
Pythagorean Identities:
2
1 + tan x =
sec 2 x
Pythagorean Identities:
2
1 + cot x =
csc 2 x
Cofunction Identities
sin (π/2 - x)
cos x
Cofunction Identities
cos (π/2 - x)
sin x
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Cofunction Identities
tan (π/2 - x)
Cofunctions of
cot x
are equal.
Complementary Angles
Sum/Difference Formulas:
sin (u + v) =
sinu cosv ± sinv cosu
Sum/Difference Formulas:
cos (u + v) =
Sum/Difference Formulas:
tan (u + v) =
cosu cosv  sinu sin v
tan u ± tan v
1  tan u tan v
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Double angle Formula
sin 2u
2 sin u cos u
Double angle Formula
cos2u - sin2u
2 cos2u - 1
1 - 2 sin2u
cos 2u
Double angle Formula
tan 2u
2 tan u
1 − tan2 u
Power Reducing Formulas
2
sin u
1 − cos2u
2
Power Reducing Formulas
2
cos u
1 + cos2u
2
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Graph of y = sin x
Graph of y = cos x
Domain
(-∞,∞)
Range
[-1,1]
Period 2π
Domain
(-∞,∞)
Range
[-1,1]
Period 2π
Domain
Graph of y = tan x
x≠
nπ
, n∍I
2
Range
(-∞,∞)
Period π
Domain
Graph of y = cot x
x≠
nπ
, n∍I
2
Range
(-∞,∞)
Period π
Domain
Graph of y = sec x
x≠
nπ
, n∍I
2
Range
|y| > 1
Period 2π
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Power Reducing Formulas
2
tan u
1 − cos2u
1 + cos2u
Product-to-Sum:
sin u sin v
1
[cos(u − v) − cos(u + v)]
2
Product-to-Sum:
cos u cos v
Product-to-Sum:
sin u cos v
Product-to-Sum:
cos u sin v
1
[cos(u − v) + cos(u + v)]
2
1
[sin(u + v) + sin(u − v)]
2
1
[sin(u + v) − sin(u − v)]
2
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Domain
Graph of y = csc x
Graph of y = sin-1 x
Graph of y = cos-1 x
Graph of y = tan-1 x
x ≠ nπ , n ∍ I
Range
|y| > 1
Period 2π
Domain
[-1,1]
Range
⎛ π π⎞
⎜− ' ⎟
⎝ 2 2⎠
Domain
[-1,1]
Range
[0,π]
Domain
(-∞,∞)
Range
⎛ π π⎞
⎜− , ⎟
⎝ 2 2⎠
Graph of y = sec-1 x
Domain
|x| >1
Range
[0,π], y ≠
π
2
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Graph of y = csc-1 x
Domain
|x| > 1
Range
⎛ π π⎞
⎜− , ⎟, y ≠ 0
⎝ 2 2⎠
Graph of y = cot-1 x
Domain
(-∞,∞)
Range
(0,π)
Graph of y = ex
Domain
(-∞,∞)
Range
(0,∞)
Graph of y = ln x
Domain
(0,∞)
Range
(-∞,∞)
Quadratic Formula
−b ± b 2 − 4ac
x=
2a
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Law of Sines
Sin A Sin B SinC
=
=
a
b
c
Law of Cosines
c 2 = a 2 + b 2 − 2abcosC
Pythagorean
Theorem
sec −1 x
−1
csc x
c2 = a 2 + b 2
1
cos
x
−1
1
sin
x
−1
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a ⋅a
x
y
x
a
y
a
(a )
x y
a
−x
log a x + log a y
a
a
x+y
x−y
a
xy
1
x
a
log a xy
12
sin −1 x + cos−1 x
π
2
tan −1 x + cot −1 x
π
2
csc −1 x + sec −1 x
π
2
log a x − log a y
⎛ x⎞
log a ⎜⎜ ⎟⎟
⎝ y⎠
log a x
b
b log a x
13
Change of Base Formula
log a x
Transformation of
Trigonometric Graphs
ln x
ln a
Vertical stretch or shrink:
reflection about x-axis
Vertical Shift
y = af (b(x + c)) + d
y = af (b(x + c)) + d
Horizontal stretch or shrink:
Horizontal Shift
reflection about y-axis
Point-Slope Equation
y = m( x − x1 ) + y1
Slope
General Linear Equation
rise Δy y2 − y1
m=
=
=
run Δx x2 − x1
Ax + By = C
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2
30°-60°-90°
Right Triangle
60°
30°
3
45°-45°-90°
Right Triangle
45°
2
1
45°
1
1