Unit Circle: Csc, Sec, & Cot Flashcards

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Questions and Answers

What is the value of csc(0Ï€)?

  • ∞
  • 0
  • 1
  • DNE (correct)

What is the value of sec(0Ï€)?

  • -1
  • 1 (correct)
  • 0
  • DNE

What is the value of cot(0Ï€)?

  • 1
  • DNE (correct)
  • ∞
  • 0

What is the value of csc(Ï€/6)?

<p>2 (B)</p> Signup and view all the answers

What is the value of sec(Ï€/6)?

<p>2√3/3 (B)</p> Signup and view all the answers

What is the value of cot(Ï€/6)?

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

What is the value of csc(Ï€/4)?

<p>√2 (D)</p> Signup and view all the answers

What is the value of sec(Ï€/4)?

<p>√2 (D)</p> Signup and view all the answers

What is the value of cot(Ï€/4)?

<p>1 (C)</p> Signup and view all the answers

What is the value of csc(Ï€/3)?

<p>2√3/3 (A)</p> Signup and view all the answers

What is the value of sec(Ï€/3)?

<p>2 (B)</p> Signup and view all the answers

What is the value of cot(Ï€/3)?

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

What is the value of csc(Ï€/2)?

<p>1 (D)</p> Signup and view all the answers

What is the value of sec(Ï€/2)?

<p>DNE (B)</p> Signup and view all the answers

What is the value of cot(Ï€/2)?

<p>0 (B)</p> Signup and view all the answers

What is the value of csc(2Ï€/3)?

<p>2√3/3 (D)</p> Signup and view all the answers

What is the value of sec(2Ï€/3)?

<p>-2 (D)</p> Signup and view all the answers

What is the value of cot(2Ï€/3)?

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

What is the value of csc(3Ï€/4)?

<p>√2 (B)</p> Signup and view all the answers

What is the value of sec(3Ï€/4)?

<p>-√2 (C)</p> Signup and view all the answers

What is the value of cot(3Ï€/4)?

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

What is the value of csc(5Ï€/6)?

<p>2 (C)</p> Signup and view all the answers

What is the value of sec(5Ï€/6)?

<p>-2√3/3 (B)</p> Signup and view all the answers

What is the value of cot(5Ï€/6)?

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

What is the value of csc(Ï€)?

<p>DNE (D)</p> Signup and view all the answers

What is the value of sec(Ï€)?

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

What is the value of cot(Ï€)?

<p>DNE (B)</p> Signup and view all the answers

What is the value of csc(7Ï€/6)?

<p>-2 (D)</p> Signup and view all the answers

What is the value of sec(7Ï€/6)?

<p>-2 (C)</p> Signup and view all the answers

What is the value of cot(7Ï€/6)?

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

What is the value of csc(5Ï€/4)?

<p>-√2 (C)</p> Signup and view all the answers

What is the value of sec(5Ï€/4)?

<p>-√2 (C)</p> Signup and view all the answers

What is the value of cot(5Ï€/4)?

<p>1 (A)</p> Signup and view all the answers

What is the value of csc(4Ï€/3)?

<p>-2√3/3 (D)</p> Signup and view all the answers

What is the value of sec(4Ï€/3)?

<p>-2 (D)</p> Signup and view all the answers

What is the value of cot(4Ï€/3)?

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

What is the value of csc(3Ï€/2)?

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

What is the value of sec(3Ï€/2)?

<p>DNE (C)</p> Signup and view all the answers

What is the value of cot(3Ï€/2)?

<p>0 (D)</p> Signup and view all the answers

What is the value of csc(5Ï€/3)?

<p>-2√3/3 (A)</p> Signup and view all the answers

What is the value of sec(5Ï€/3)?

<p>1 (D)</p> Signup and view all the answers

What is the value of cot(5Ï€/3)?

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

What is the value of csc(7Ï€/4)?

<p>-√2 (C)</p> Signup and view all the answers

What is the value of sec(7Ï€/4)?

<p>√2 (C)</p> Signup and view all the answers

What is the value of cot(7Ï€/4)?

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

What is the value of csc(11Ï€/6)?

<p>-2 (D)</p> Signup and view all the answers

What is the value of sec(11Ï€/6)?

<p>2√3/3 (B)</p> Signup and view all the answers

What is the value of cot(11Ï€/6)?

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

Flashcards

csc(0Ï€)

Cosecant of 0Ï€ is undefined.

sec(0Ï€)

Secant of 0Ï€ is 1.

cot(0Ï€)

Cotangent of 0Ï€ is undefined.

csc(Ï€/6)

Cosecant of π/6 is 2.

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sec(Ï€/6)

Secant of π/6 is 2√3/3.

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cot(Ï€/6)

Cotangent of π/6 is √3.

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csc(Ï€/4)

Cosecant of π/4 is √2.

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sec(Ï€/4)

Secant of π/4 is √2.

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cot(Ï€/4)

Cotangent of π/4 is 1.

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csc(Ï€/3)

Cosecant of π/3 is 2√3/3.

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sec(Ï€/3)

Secant of π/3 is 2.

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cot(Ï€/3)

Cotangent of π/3 is √3/3.

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csc(Ï€/2)

Cosecant of π/2 is 1.

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sec(Ï€/2)

Secant of π/2 is undefined.

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cot(Ï€/2)

Cotangent of π/2 is 0.

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csc(Ï€)

Cosecant of π is undefined.

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sec(Ï€)

Secant of π is -1.

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cot(Ï€)

Cotangent of π is undefined.

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csc(3Ï€/2)

Cosecant of 3Ï€/2 is -1.

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sec(3Ï€/2)

Secant of 3Ï€/2 is undefined.

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cot(3Ï€/2)

Cotangent of 3Ï€/2 is 0.

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Study Notes

Cosecant, Secant, and Cotangent Values at Key Angles

  • Csc(0Ï€) is undefined (DNE).
  • Sec(0Ï€) equals 1.
  • Cot(0Ï€) is undefined (DNE).

Angle π/6 Values

  • Csc(Ï€/6) equals 2.
  • Sec(Ï€/6) equals 2√3/3.
  • Cot(Ï€/6) equals √3.

Angle π/4 Values

  • Csc(Ï€/4) equals √2.
  • Sec(Ï€/4) equals √2.
  • Cot(Ï€/4) equals 1.

Angle π/3 Values

  • Csc(Ï€/3) equals 2√3/3.
  • Sec(Ï€/3) equals 2.
  • Cot(Ï€/3) equals √3/3.

Angle π/2 Values

  • Csc(Ï€/2) equals 1.
  • Sec(Ï€/2) is undefined (DNE).
  • Cot(Ï€/2) equals 0.

Angle 2Ï€/3 Values

  • Csc(2Ï€/3) equals 2√3/3.
  • Sec(2Ï€/3) equals -2.
  • Cot(2Ï€/3) equals -√3/3.

Angle 3Ï€/4 Values

  • Csc(3Ï€/4) equals √2.
  • Sec(3Ï€/4) equals -√2.
  • Cot(3Ï€/4) equals -1.

Angle 5Ï€/6 Values

  • Csc(5Ï€/6) equals 2.
  • Sec(5Ï€/6) equals -2√3/3.
  • Cot(5Ï€/6) equals -√3.

Angle π Values

  • Csc(Ï€) is undefined (DNE).
  • Sec(Ï€) equals -1.
  • Cot(Ï€) is undefined (DNE).

Angle 7Ï€/6 Values

  • Csc(7Ï€/6) equals -2.
  • Sec(7Ï€/6) equals -2√3/3.
  • Cot(7Ï€/6) equals √3.

Angle 5Ï€/4 Values

  • Csc(5Ï€/4) equals -√2.
  • Sec(5Ï€/4) equals -√2.
  • Cot(5Ï€/4) equals 1.

Angle 4Ï€/3 Values

  • Csc(4Ï€/3) equals -2√3/3.
  • Sec(4Ï€/3) equals -2.
  • Cot(4Ï€/3) equals √3/3.

Angle 3Ï€/2 Values

  • Csc(3Ï€/2) equals -1.
  • Sec(3Ï€/2) is undefined (DNE).
  • Cot(3Ï€/2) equals 0.

Angle 5Ï€/3 Values

  • Csc(5Ï€/3) equals -2√3/3.
  • Sec(5Ï€/3) equals 2.
  • Cot(5Ï€/3) equals -√3/3.

Angle 7Ï€/4 Values

  • Csc(7Ï€/4) equals -√2.
  • Sec(7Ï€/4) equals √2.
  • Cot(7Ï€/4) equals -1.

Angle 11Ï€/6 Values

  • Csc(11Ï€/6) equals -2.
  • Sec(11Ï€/6) equals 2√3/3.
  • Cot(11Ï€/6) equals -√3.

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