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Marina86 [1]
2 years ago
11

For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?

Mathematics
1 answer:
rosijanka [135]2 years ago
7 0

Answer:

  • sinθ = 3/5
  • cosθ = 4/5

<h3>Given </h3>
  • Point (16, 12)

<h3>To find </h3>
  • Sine and cosine of the angle, using the given coordinates

<h3>Solution</h3>

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:

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

Find sine:

  • <em>sine = opposite/hypotenuse</em>
  • sinθ = 12/20 = 3/5

Find cosine:

  • <em>cosine = adjacent/hypotenuse</em>
  • cosθ = 16/20 = 4/5

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