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Find sinθ and cosθ if the terminal side of θ lies along the line y=2x in quadrant I.

User Jahnold
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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

User Mochidino
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