Answer:
Since the terminal side of θ lies along the line y = 2x in quadrant I, we can draw a right triangle with the hypotenuse along the line y = 2x, the adjacent side along the x-axis, and the opposite side along the y-axis. The angle θ is the angle between the hypotenuse and the x-axis.
We can use the Pythagorean theorem to find the length of the hypotenuse:
h^2 = (2x)^2 + x^2
h^2 = 4x^2 + x^2
h^2 = 5x^2
h = x√5
Now we can use the definitions of sine and cosine to find sinθ and cosθ:
sinθ = opposite/hypotenuse = x/x√5 = √(1/5)
cosθ = adjacent/hypotenuse = 2x/x√5 = 2/√5
Therefore, sinθ = √(1/5) and cosθ = 2/√5.
hope it helps you