The terminal side of an angle θ in standard position intersects the unit circle at

36

85

,

77

85

. What is cos(θ)?

Write your answer in simplified, rationalized form.

Cos θ = (36/85) in simplified rationalized form

Cos θ = 0.4235

Step-by-step 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!!!

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)