Answer:
Cos θ = (36/85) in simplified rationalized form
Cos θ = 0.4235
Explanation:
The image of the description is attached to this solution.
The terminal side of an angle is the side that is directly opposite to the angle.
Let the point where the terminal side intersects the unit circle be (x, y)
The length of the radius of the circle = 1 unit
This setup of the terminal side meeting the radius gives a right angle triangle.
With hypotenuse = radius = 1.
It is evident that the length of the two other sides are (36/85) and (77/85) respectively.
To check, we use the Pythagoras theorem.
x² + y² = r²
(36/85)² + (77/85)² = r²
(36² + 77²)/85² = r²
(1296 + 5929)/7225 = r²
(7225/7225) = r²
r = 1 unit!! As predicted by the question.
So,
cos θ = (Adj/Hyp)
Adj = (36/85)
Hyp = 1
So,
Cos θ = (36/85) = 0.4235
Hope this Helps!!!