Six Trig Finctions

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The Map of Trigonometric Functions

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L1TM

par P F

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par David Lanier

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par Sebastian Acosta

Six Trig Finctions

Tan

Y/X

Half Angle: tan^2 u=1-cos(2u)/1+cosine(2u)

Reciprocal: tan u=1/cot u

Pythagorean: 1+tan^2u=sec^2u

Cosine

X/r

Half Angle: cosine^2 u=1+cosine(2u)/2

Reciprocal: cos u=1/sec u

Sine

Y/r

Half Angle: sine^2 u=1-cosine(2u)/2

Reciprocal: sine u=1/cosine u

Subtopic

Pythagorean: sine^2 u + cosine^2u=1

Cotangeant

X/Y

Reciprocal: cot u = 1/tan u

Pythagorean: 1 + cot^2 u = csc^2 u

Secant

r/X

Reciprocal: sec u = 1/ cos u

Pythagorean: sec^2 u = 1 + tan^2 u

Cosecant

r/Y

Reciprocal: csc u = 1/sin u

Pythagorean: csc^2 u = 1 + cot^2 u