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Pre-Calculus sin/cos, domain/range, and identities

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domain of sin
all θ
domain of cos
all θ
domain of tan
θ does not = Ϭ/2 + nϬ
domain of cot
θ does not = nϬ
domain of sec
θ does not = Ϭ/2 + nϬ
domain of csc
θ does not = nϬ
range of sin
|sin θ| ≤ 1
range of cos
|cos θ| ≤ 1
range of tan
all reals
range of cot
all reals
range of sec
|sec θ| ≥ 1
range of csc
|csc θ| ≥ 1
domain of inverse sin
-1 ≤ x ≤ 1
domain of inverse cos
-1 ≤ x ≤ 1
domain of inverse tan
all real x
range of inverse sin
-π/2 ≤ y ≤ π/2
range of inverse cos
0 ≤ y ≤ π
range of inverse tan
-Ϭ/2 < y < Ϭ/2
sine
y/r
cosine
x/r
tangent
y/x
cosecant
r/y
secant
r/x
cotangent
x/y
30º
Ï€/6
(√3/2, 1/2)
45º
Ï€/4
(√2/2, √2/2)
60º
Ï€/3
(1/2, √3/2)
90º
Ϭ/2
(0, 1)
120º
2Ï€/3
(-1/2, √3/2)
135º
3Ï€/4
(-√2/2, √2/2)
150º
5Ï€/6
(-√3/2, 1/2)
180º
Ϭ
(-1, 0)
210º
7Ï€/6
(-√3/2, -1/2)
225º
5Ï€/4
(-√2/2, -√2/2)
240º
4Ï€/3
(-1/2, -√3/2)
270º
3Ϭ/2
(0, -1)
300º
5Ï€/3
(1/2, -√3/2)
315º
7Ï€/4
(√2/2, -√2/2)
330º
11Ï€/6
(√3/2, -1/2)
360º

(1, 0)
Arc Length (for rads)
s = rθ
Arc Length (for degrees)
s = θ/360º x 2Ϭr/1
Area of a sector (for degrees)
K = θ/360º x Ϭr²
Area of a sector (for rads)
K = 1/2 r² θ
Area of a sector (for arc length)
K = 1/2 r s
degrees to rads
(degreeº) x Ϭ/180º
rads to degrees
(rad) x 180º/Ϭ
reciprocal of csc x
1/sin x
reciprocal of sec x
1/cos x
reciprocal of cot x
1/tan x
reciprocal of sin x
1/csc x
reciprocal of cos x
1/sec x
reciprocal of tan x
1/cot x
Quotient of tan x
sin x/cos x
Quotient of cot x
cos x/sin x
cos (-x) =
cos x
sin (-x) =
- sin x
csc (-x) =
-csc x
tan (-x) =
-tan x
sec (-x) =
sec x
cot (-x) =
-cot x
Pythagorian and variations of sec²x
1 + tan²x = sec²x
1 = sec²x - tan²x
Pythagorian and variations of csc²x
1 + cot²x = csc²x
1 = csc²x - cot²x
Pythagorian and variations of sin²x
1 - cos²x = sin²x
1 = sin²x + cos²x
Pythagorian and variations of cos²x
1 - sin²x = cos²x
sin²x - 1 = -cos²x
1 = sin²x + cos²x
Cofunction of sin x
cos (90º - θ)
Cofunction of tan x
cot (90º - θ)
Cofunction of sec x
csc (90º - θ)

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