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For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?
for the point (16,12) find sin theta and cos theta

Respuesta :

mhanifa

Answer:

  • sinθ = 3/5
  • cosθ = 4/5

Given

  • Point (16, 12)

To find

  • Sine and cosine of the angle, using the given coordinates

Solution

Since both of the coordinates are positive, we have:

  • the angle θ is in the first quadrant, both sine and cosine have positive values;
  • the x-coordinate determines the value of adjacent leg;
  • the y-coordinate determines the value of opposite leg.

Find the hypotenuse of the right triangle using values of both legs:

  • [tex]h=\sqrt{ x^2+y^2}=\sqrt{16^2+12^2}= \sqrt{400} =20[/tex]

Find sine:

  • sine = opposite/hypotenuse
  • sinθ = 12/20 = 3/5

Find cosine:

  • cosine = adjacent/hypotenuse
  • cosθ = 16/20 = 4/5

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