Formulas for DUMMIES
Scroll down! I have given you all of the formulas you need for your Trigonometry course, so you do not have to waste your time.
Basic Trigonometric Functions:
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sin θ = Opposite Side/Hypotenuse
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cos θ = Adjacent Side/Hypotenuse
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tan θ = Opposite Side/Adjacent Side
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sec θ = Hypotenuse/Adjacent Side
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cosec θ = Hypotenuse/Opposite Side
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cot θ = Adjacent Side/Opposite Side
Reciprocal Identities:
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cosec θ = 1/sin θ
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sec θ = 1/cos θ
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cot θ = 1/tan θ
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sin θ = 1/cosec θ
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cos θ = 1/sec θ
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tan θ = 1/cot θ
Periodicity Identities (in Radians):
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sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
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sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
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sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A
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sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
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sin (π – A) = sin A & cos (π – A) = – cos A
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sin (π + A) = – sin A & cos (π + A) = – cos A
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sin (2π – A) = – sin A & cos (2π – A) = cos A
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sin (2π + A) = sin A & cos (2π + A) = cos A
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Co-function Identities (in Degrees):
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sin(90°−x) = cos x
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cos(90°−x) = sin x
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tan(90°−x) = cot x
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cot(90°−x) = tan x
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sec(90°−x) = csc x
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csc(90°−x) = sec x
Sum & Difference Identities:
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sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
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cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
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tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)
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sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
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cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
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tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)
Triple Angle Identities:
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Sin 3x = 3sin x – 4sin3x
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Cos 3x = 4cos3x-3cos x
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Tan 3x = [3tanx-tan3x]/[1-3tan2x]
Inverse Trigonometry Formula:
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sin-1 (–x) = – sin-1 x
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cos-1 (–x) = π – cos-1 x
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tan-1 (–x) = – tan-1 x
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cosec-1 (–x) = – cosec-1 x
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sec-1 (–x) = π – sec-1 x
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cot-1 (–x) = π – cot-1 x
Double Angle Identities:
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sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
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cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]
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cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
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tan(2x) = [2tan(x)]/ [1−tan2(x)]
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sec (2x) = sec2 x/(2-sec2 x)
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csc (2x) = (sec x. csc x)/2
