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# Content

```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 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 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 Product of Cosine and Sine

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

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