Trigonometric Functions Quiz

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Questions and Answers

Cotangent function'un formülünü hangi işlemden elde edilir?

  • tan(θ) / sin(θ)
  • 1 / tan(θ) (correct)
  • sin(θ) / cos(θ)
  • cos(θ) / sin(θ)

Sinüs function'un değer aralığı nedir?

  • [0, 1]
  • (0, 1]
  • (-∞, ∞)
  • [-1, 1] (correct)

Tanjant function'un tanımını verilen seçeneklerden hangisi sağlar?

  • the ratio of the sine to the cosine (correct)
  • the ratio of the opposite side to the adjacent side
  • the ratio of the opposite side to the hypotenuse
  • the ratio of the adjacent side to the hypotenuse

Cosecant function'un hangi değerde undefined olur?

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

Cosine function'un değeri, 0 derece için nedir?

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

Cotangent function'un hangi özelliği, -θ için -cot(θ) olarak ifade edilir?

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

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Study Notes

Trigonometric Functions

Cotangent (cot)

  • Definition: The reciprocal of the tangent function
  • Formula: cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ)
  • Range: (-∞, ∞)
  • Properties:
    • cot(0) = undefined
    • cot(π/2) = 0
    • cot(-θ) = -cot(θ)

Sine (sin)

  • Definition: The ratio of the opposite side to the hypotenuse in a right-angled triangle
  • Formula: sin(θ) = opposite side / hypotenuse
  • Range: [-1, 1]
  • Properties:
    • sin(0) = 0
    • sin(π/2) = 1
    • sin(-θ) = -sin(θ)

Cosine (cos)

  • Definition: The ratio of the adjacent side to the hypotenuse in a right-angled triangle
  • Formula: cos(θ) = adjacent side / hypotenuse
  • Range: [-1, 1]
  • Properties:
    • cos(0) = 1
    • cos(π/2) = 0
    • cos(-θ) = cos(θ)

Tangent (tan)

  • Definition: The ratio of the sine to the cosine
  • Formula: tan(θ) = sin(θ) / cos(θ)
  • Range: (-∞, ∞)
  • Properties:
    • tan(0) = 0
    • tan(π/2) = undefined
    • tan(-θ) = -tan(θ)

Cosecant (csc)

  • Definition: The reciprocal of the sine function
  • Formula: csc(θ) = 1 / sin(θ)
  • Range: (-∞, -1] ∪ [1, ∞)
  • Properties:
    • csc(0) = undefined
    • csc(π/2) = 1
    • csc(-θ) = -csc(θ)

Secant (sec)

  • Definition: The reciprocal of the cosine function
  • Formula: sec(θ) = 1 / cos(θ)
  • Range: (-∞, -1] ∪ [1, ∞)
  • Properties:
    • sec(0) = 1
    • sec(π/2) = undefined
    • sec(-θ) = sec(θ)

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