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What are the six trigonometric ratios associated with an angle in a triangle when using the sides of the triangle in calculus?

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Final answer:

The six trigonometric ratios associated with an angle in a triangle are sine, cosine, tangent, cosecant, secant, and cotangent.

Step-by-step explanation:

The six trigonometric ratios associated with an angle in a triangle are the following:

  • Sine (sin): The ratio of the opposite side to the hypotenuse of the triangle. It is calculated as sin(A) = opposite/hypotenuse.
  • Cosine (cos): The ratio of the adjacent side to the hypotenuse of the triangle. It is calculated as cos(A) = adjacent/hypotenuse.
  • Tangent (tan): The ratio of the opposite side to the adjacent side of the triangle. It is calculated as tan(A) = opposite/adjacent.
  • Cosecant (csc): The reciprocal of the sine. It is calculated as csc(A) = hypotenuse/opposite.
  • Secant (sec): The reciprocal of the cosine. It is calculated as sec(A) = hypotenuse/adjacent.
  • Cotangent (cot): The reciprocal of the tangent. It is calculated as cot(A) = adjacent/opposite.

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