Question

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

Answer 1

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:

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

Find sine:

• sine = opposite/hypotenuse

• sinθ = 12/20 = 3/5

Find cosine:

• cosine = adjacent/hypotenuse

• cosθ = 16/20 = 4/5