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Trigonometry
  The Trigonometric Functions
  The Values of Common Angles of Trigonometric Functions
  The Laws of Trigonometric Functions
  The Law of Sines
  The Law of Cosines
  The Trigonometric Identities
  The Identities of Negative Angle
  The Identities of CoFunction
  The Identities of Periodicity
  The Reduction Formulas of Trigonometric Functions
  The Identities of Angle Sum and Difference
  The Pythagorean identity
  The Identities of Double Angle
  The Identities of Half Angle
  The Product of Cosine and Sine

Trigonometry

The Trigonometric Functions

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The Values of Common Angles of Trigonometric Functions

Degrees Radians sin θ cos θ tan θ cot θ sec θ csc θ
0 0 0 1 0 undefined 1 undefined
30 π/6 1/2 √3/2 √3/3 √3 2√3/3 2
45 π/4 √2/2 √2/2 1 1 √2 √2
60 π/3 √3/2 1/2 √3 √3/3 2 2√3/3
90 π/2 1 0 undefined 0 undefined 1
120 2π/3 √3/2 -1/2 -√3 -√3/3 -2 2√3/3
135 3π/4 √2/2 -√2/2 -1 -1 -√2 √2
150 5π/6 1/2 -√3/2 -√3/3 -√3 -2√3/3 2
180 π 0 -1 0 undefined -1 undefined
210 7π/6 -1/2 -√3/2 √3/3 √3 -2√3/3 -2
225 5π/4 -√2/2 -√2/2 1 1 -√2 -√2
240 4π/3 -√3/2 -1/2 √3 √3/3 -2 -2√3/3
270 3π/2 -1 0 undefined 0 undefined -1
300 5π/3 -√3/2 1/2 -√3 -√3/3 2 -2√3/3
315 7π/4 -√2/2 √2/2 -1 -1 √2 -√2
330 11π/6 -1/2 √3/2 -√3/3 -√3 2√3/3 -2
360 0 1 0 undefined 1 undefined

The Laws of Trigonometric Functions

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The Law of Sines

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The Law of Cosines

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The Trigonometric Identities

The Identities of Negative Angle

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The Identities of CoFunction

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The Identities of Periodicity

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The Reduction Formulas of Trigonometric Functions

a sin cos tan cot sec csc
Radians α-θ α+θ α-θ α+θ α-θ α+θ α-θ α+θ α-θ α+θ α-θ α+θ
0 -sin θ sin θ cos θ cos θ -tan θ tan θ -cot θ cot θ sec θ sec θ -csc θ csc θ
π/2 cos θ cos θ sin θ -sin θ cot θ -cot θ tan θ -tan θ csc θ -csc θ sec θ sec θ
π sin θ -sin θ -cos θ -cos θ -tan θ tan θ -cot θ cot θ -sec θ -sec θ csc θ -csc θ
3π/2 -cos θ -cos θ -sin θ sin θ cot θ -cot θ tan θ -tan θ -csc θ csc θ -sec θ -sec θ
2πn -sin θ sin θ cos θ cos θ -tan θ tan θ -cot θ cot θ sec θ sec θ -csc θ csc θ

The Identities of Angle Sum and Difference

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The Pythagorean identity

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The Identities of Double Angle

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The Identities of Half Angle

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The Product of Cosine and Sine

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ID: 100900012 Last Updated: 12/25/2011 Revision: 1

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