Trigonometry: Tangent and Cotangent Values

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Questions and Answers

What is the definition of Tangent (tan)?

A Tangent (tan) is the Sine (sin), divided by the Cosine (cos). (sin)/(cos)

What is the definition of Cotangent (cot)?

A Cotangent (cot) is the Cosine (cos) divided by the Sine (sin). (cos)/(sin)

What is tan(0)?

0

What is tan(Ï€/2)?

<p>undefined</p> Signup and view all the answers

What is tan(Ï€)?

<p>0</p> Signup and view all the answers

What is tan(3Ï€/2)?

<p>undefined</p> Signup and view all the answers

What is tan(2Ï€)?

<p>0</p> Signup and view all the answers

What is tan(Ï€/6)?

<p>√3/3</p> Signup and view all the answers

What is tan(Ï€/4)?

<p>1</p> Signup and view all the answers

What is tan(Ï€/3)?

<p>√3</p> Signup and view all the answers

What is tan(2Ï€/3)?

<p>-√3</p> Signup and view all the answers

What is tan(3Ï€/4)?

<p>-1</p> Signup and view all the answers

What is tan(5Ï€/6)?

<p>-√3/3</p> Signup and view all the answers

What is tan(7Ï€/6)?

<p>√3/3</p> Signup and view all the answers

What is tan(5Ï€/4)?

<p>1</p> Signup and view all the answers

What is tan(4Ï€/3)?

<p>√3</p> Signup and view all the answers

What is tan(5Ï€/3)?

<p>-√3</p> Signup and view all the answers

What is tan(7Ï€/4)?

<p>-1</p> Signup and view all the answers

What is tan(11Ï€/6)?

<p>-√3/3</p> Signup and view all the answers

What is cot(0)?

<p>undefined</p> Signup and view all the answers

What is cot(Ï€/2)?

<p>0</p> Signup and view all the answers

What is cot(Ï€)?

<p>undefined</p> Signup and view all the answers

What is cot(3Ï€/2)?

<p>0</p> Signup and view all the answers

What is cot(2Ï€)?

<p>undefined</p> Signup and view all the answers

What is cot(Ï€/6)?

<p>√3</p> Signup and view all the answers

What is cot(Ï€/4)?

<p>1</p> Signup and view all the answers

What is cot(Ï€/3)?

<p>√3/3</p> Signup and view all the answers

What is cot(2Ï€/3)?

<p>-√3/3</p> Signup and view all the answers

What is cot(3Ï€/4)?

<p>-1</p> Signup and view all the answers

What is cot(5Ï€/6)?

<p>-√3</p> Signup and view all the answers

What is cot(7Ï€/6)?

<p>√3</p> Signup and view all the answers

What is cot(5Ï€/4)?

<p>1</p> Signup and view all the answers

What is cot(4Ï€/3)?

<p>√3/3</p> Signup and view all the answers

What is cot(5Ï€/3)?

<p>-√3/3</p> Signup and view all the answers

What is cot(7Ï€/4)?

<p>-1</p> Signup and view all the answers

What is cot(11Ï€/6)?

<p>-√3</p> Signup and view all the answers

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Study Notes

Definitions

  • Tangent (tan) is defined as the ratio of the sine (y-coordinate) to cosine (x-coordinate) of an angle: tan(θ) = sin(θ) / cos(θ).
  • Cotangent (cot) is defined as the ratio of cosine (x-coordinate) to sine (y-coordinate) of an angle: cot(θ) = cos(θ) / sin(θ).

Tangent Values

  • tan(0) equals 0.
  • tan(Ï€/2) is undefined.
  • tan(Ï€) equals 0.
  • tan(3Ï€/2) is undefined.
  • tan(2Ï€) equals 0.
  • tan(Ï€/6) equals √3/3.
  • tan(Ï€/4) equals 1.
  • tan(Ï€/3) equals √3.
  • tan(2Ï€/3) equals -√3.
  • tan(3Ï€/4) equals -1.
  • tan(5Ï€/6) equals -√3/3.
  • tan(7Ï€/6) equals √3/3.
  • tan(5Ï€/4) equals 1.
  • tan(4Ï€/3) equals √3.
  • tan(5Ï€/3) equals -√3.
  • tan(7Ï€/4) equals -1.
  • tan(11Ï€/6) equals -√3/3.

Cotangent Values

  • cot(0) is undefined.
  • cot(Ï€/2) equals 0.
  • cot(Ï€) is undefined.
  • cot(3Ï€/2) equals 0.
  • cot(2Ï€) is undefined.
  • cot(Ï€/6) equals √3.
  • cot(Ï€/4) equals 1.
  • cot(Ï€/3) equals √3/3.
  • cot(2Ï€/3) equals -√3/3.
  • cot(3Ï€/4) equals -1.
  • cot(5Ï€/6) equals -√3.
  • cot(7Ï€/6) equals √3.
  • cot(5Ï€/4) equals 1.
  • cot(4Ï€/3) equals √3/3.
  • cot(5Ï€/3) equals -√3/3.
  • cot(7Ï€/4) equals -1.
  • cot(11Ï€/6) equals -√3.

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