Trigonometric Formula Sheet Page 2
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1
2Double-Angle Formulas
Sum Formulas
1
1
sin2x = 2sin x cos x
sin x + sin y = 2sin
(x + y)cos
(x − y)
2
2
2
2
cos2x = cos
x − sin
x
1
1
sin x − sin y = 2sin
(x − y)cos
(x + y)
2
cos2x = 2cos
x − 1
2
2
2
1
1
cos2x = 1− 2sin
x
cos x + cos y = 2 cos
(x + y) cos
(x − y)
2
2
2tan x
tan 2x =
2
1− tan
x
1
1
cos x − cos y = −2sin
(x + y)sin
(x − y)
2
2
Half-Angle Formulas
1
1− cos x
Inverse Functions
sin
x = ±
2
2
−1
if and only if x = sin y
y = sin
x
π
π
1
1+ cos x
and −
≤ y ≤
cos
x = ±
2
2
2
2
−1
if and only if x = cos y
1
sin x
y = cos
x
tan
x =
and 0 ≤ y ≤ π
2
1 + cos x
−1
1
1− cos x
if and only if x = tan y
y = tan
x
tan
x =
π
π
2
sin x
and −
≤ y ≤
2
2
1
1− cos x
tan
x =
2
1+ cos x
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Product Formulas
SOH-CAH-TOA
1
sin x sin y =
[cos(x − y) − cos(x + y)]
opposite
2
sin x =
hypotenuse
1
cos x cos y =
[cos(x + y) + cos(x − y)]
adjacent
2
cos x =
hypotenuse
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1
sin x cos y =
[sin(x + y) + sin(x − y)]
opposite
2
tan x =
adjacent
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