163k views
2 votes
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

1 Answer

12 votes

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:


  • h=√( x^2+y^2)=√(16^2+12^2)= √(400) =20

Find sine:

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

Find cosine:

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

User Haravikk
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories